Spectroscopic Ellipsometry for Photovoltaics: Volume 2: Applications and Optical Data of Solar Cell Materials [1st ed.] 978-3-319-95137-9, 978-3-319-95138-6

Table of contents :
Front Matter ....Pages i-xxi
Introduction (Hiroyuki Fujiwara)....Pages 1-26
Front Matter ....Pages 27-27
Analysis of Optical and Recombination Losses in Solar Cells (Hiroyuki Fujiwara, Akihiro Nakane, Daisuke Murata, Hitoshi Tampo, Takuya Matsui, Hajime Shibata)....Pages 29-82
Optical Simulation of External Quantum Efficiency Spectra (Prakash Koirala, Abdel-Rahman A. Ibdah, Puruswottam Aryal, Puja Pradhan, Zhiquan Huang, Nikolas J. Podraza et al.)....Pages 83-138
Characterization of Textured Structures (Hiroyuki Fujiwara, Yuichiro Sago)....Pages 139-168
On-line Monitoring of Photovoltaics Production (Ambalanath Shan, Jie Chen, Prakash Koirala, Kenneth R. Kormanyos, Nikolas J. Podraza, Robert W. Collins)....Pages 169-207
Real Time Measurement, Monitoring, and Control of CuIn1−xGaxSe2 by Spectroscopic Ellipsometry (Puja Pradhan, Abdel-Rahman A. Ibdah, Puruswottam Aryal, Dinesh Attygalle, Nikolas J. Podraza, Sylvain Marsillac et al.)....Pages 209-253
Real Time and Mapping Spectroscopic Ellipsometry of Hydrogenated Amorphous and Nanocrystalline Si Solar Cells (Zhiquan Huang, Lila R. Dahal, Sylvain Marsillac, Nikolas J. Podraza, Robert W. Collins)....Pages 255-315
Front Matter ....Pages 317-317
Inorganic Semiconductors and Passivation Layers (Akihiro Nakane, Shohei Fujimoto, Gerald E. Jellison Jr., Craig M. Herzinger, James N. Hilfiker, Jian Li et al.)....Pages 319-426
Organic Semiconductors (Takemasa Fujiseki, Shohei Fujimoto, Mariano Campoy-Quiles, Maria Isabel Alonso, Takurou N. Murakami, Tetsuhiko Miyadera et al.)....Pages 427-469
Organic-Inorganic Hybrid Perovskites (Shohei Fujimoto, Takemasa Fujiseki, Masato Tamakoshi, Akihiro Nakane, Tetsuhiko Miyadera, Takeshi Sugita et al.)....Pages 471-493
Transparent Conductive Oxides (Akihiro Nakane, Shohei Fujimoto, Masato Tamakoshi, Takashi Koida, James N. Hilfiker, Gerald E. Jellison Jr. et al.)....Pages 495-541
Metals (Shohei Fujimoto, Takemasa Fujiseki, Hiroyuki Fujiwara)....Pages 543-574
Substrates and Coating Layers (Shohei Fujimoto, Takemasa Fujiseki, James N. Hilfiker, Nina Hong, Mariano Campoy-Quiles, Hiroyuki Fujiwara)....Pages 575-608
Back Matter ....Pages 609-616

Citation preview

Springer Series in Optical Sciences 214

Hiroyuki Fujiwara Robert W. Collins Editors

Spectroscopic Ellipsometry for Photovoltaics Volume 2: Applications and Optical Data of Solar Cell Materials

Springer Series in Optical Sciences Volume 214

Founded by H. K. V. Lotsch Editor-in-chief William T. Rhodes, Florida Atlantic University, Boca Raton, FL, USA Series editors Ali Adibi, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA Toshimitsu Asakura, Hokkai-Gakuen University, Sapporo, Hokkaido, Japan Theodor W. Hänsch, Max-Planck-Institut für Quantenoptik, Garching, Bayern, Germany Ferenc Krausz, Garching, Bayern, Germany Barry R. Masters, Cambridge, MA, USA Katsumi Midorikawa, Laser Technology Laboratory, RIKEN Advanced Science Institute, Saitama, Japan Bo A. J. Monemar, Department of Physics and Measurement Technology, Linköping University, Linköping, Sweden Herbert Venghaus, Ostseebad Binz, Germany Horst Weber, Berlin, Germany Harald Weinfurter, München, Germany

Springer Series in Optical Sciences is led by Editor-in-Chief William T. Rhodes, Georgia Institute of Technology, USA, and provides an expanding selection of research monographs in all major areas of optics: – – – – – – – –

lasers and quantum optics ultrafast phenomena optical spectroscopy techniques optoelectronics information optics applied laser technology industrial applications and other topics of contemporary interest.

With this broad coverage of topics the series is useful to research scientists and engineers who need up-to-date reference books.

More information about this series at http://www.springer.com/series/624

Hiroyuki Fujiwara Robert W. Collins •

Editors

Spectroscopic Ellipsometry for Photovoltaics Volume 2: Applications and Optical Data of Solar Cell Materials

123

Editors Hiroyuki Fujiwara Department of Electrical, Electronic and Computer Engineering Gifu University Gifu, Japan

Robert W. Collins Department of Physics and Astronomy The University of Toledo Toledo, OH, USA

ISSN 0342-4111 ISSN 1556-1534 (electronic) Springer Series in Optical Sciences ISBN 978-3-319-95137-9 ISBN 978-3-319-95138-6 (eBook) https://doi.org/10.1007/978-3-319-95138-6 Library of Congress Control Number: 2018931482 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

There has been a strong concern for global climate change particularly in recent years, as disasters induced by extreme weathers appear to increase year by year. One solution for the environmental crisis is a clean energy source, and solar cell production increased drastically in the last decade. Although solar cells are generally viewed as pure semiconductor devices, solar cells are essentially optical devices and, for the optimization and interpretation of solar cell performance, the knowledge for the optical processes in the devices is critical. In particular, the optical characteristics of solar cell component layers and the device configurations affect the resulting conversion efficiencies directly and thus the determination of the optical properties and structures is of significant importance. Recently, for the characterization of material optical properties and structures, spectroscopic ellipsometry (SE) technique is employed more widely in solar cell researches. In particular, ellipsometry has great advantages over other characterization techniques, including accurate optical constant determination, very fast spectral measurements within a few seconds, extremely high thickness sensitivity, and large-area characterization of optical characteristics and structures. Thus, SE has a large potential as a monitoring tool of mass production. Moreover, SE characterization can be made even for textured structures incorporated into actual devices. In fact, for the production of crystalline and amorphous Si solar cells, SE-based measurement systems have often been used. Based on the optical constants extracted from SE characterizations, explicit device characterization/simulation can further be performed. From such analyses, we can determine the current loss mechanisms and predict the conversion efficiency of specific solar cells. In general, practical solar cell optimization relies heavily on try-and-error approach and maximizing conversion efficiencies is very time-consuming. However, the solar cell optimization using device simulation is expected to be far more effective if compared with conventional approach. In the second volume of Spectroscopic Ellipsometry for Photovoltaics, we focused on SE application on solar cell characterization. In particular, this book consists of the following two major parts: spectroscopic ellipsometry applications for which more advanced instrumentation and analyses are required (Part I) and the v

vi

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complete optical functions of solar cell component layers (Part II), which are crucial for ellipsometry analyses and optical simulations of devices. Specifically, after an introductory chapter which gives (i) a general introduction for photovoltaic devices and (ii) an overview over the contents of the subsequent chapters in the book (Chap. 1), in Part I, more advanced applications for external quantum efficiency (EQE) analyses (Chaps. 2 and 3) and structural characterization (Chaps. 4–7) are described. The EQE analysis is of significant importance to find the current loss mechanism in the devices (Chap. 2) and the optical effects of each component layer (Chap. 3). By employing advanced optical modeling techniques, even textured multilayer structures can be studied by ellipsometry (Chap. 4). The examples of online monitoring of solar cell module production (Chap. 5), real-time control of thin layer growth (Chap. 6), and the mapping characterization of solar cell devices (Chap. 7) are also provided in Part I. In Part II, tabulated optical constants and completely parameterized parameters for 148 materials used in various photovoltaic devices are summarized. The solar cell materials covered in Part II include inorganic semiconductors (Chap. 8), organic semiconductors (Chap. 9), hybrid perovskite materials (Chap. 10), transparent conductive oxides (Chap. 11), metals (Chap. 12), and substrates (Chap. 13). All the dielectric functions described in Part II are modeled using only three models, i.e., the Sellmeier, Tauc–Lorentz, and Drude models. By employing the optical data described in Part II, accurate ellipsometry characterization and optical simulation can be performed rather easily. Gifu, Japan Toledo, USA

Hiroyuki Fujiwara Robert W. Collins

Acknowledgements

The editors would like to thank all authors for their great contributions and helpful suggestions. Concerning the optical data of numerous solar cell component layers, HF and RWC are especially grateful to Drs. Gerald E. Jellison Jr., James N. Hilfiker, Craig M. Herzinger, Mariano Campoy-Quiles, Nina Hong, Takashi Koida, Jian Li, Hitoshi Tampo, and Maria I. Alonso for their continuous support and encouragement during the preparation of this book that took more than 3 years. HF thanks Drs. Shigeru Niki and Koji Matsubara for their kind support. HF gratefully acknowledges Dr. Claus E. Ascheron who has supported the publication of this book. HF wishes to express sincere gratitude to Shohei Fujimoto, Akihiro Nakane, Takemasa Fujiseki, Masato Kato, Mitsutoshi Nishiwaki, and Masayuki Kozawa for their enthusiastic efforts for the preparation of this book. RWC acknowledges data and graphics assistance from chapter contributors, Drs. Puruswottam Aryal, Dinesh Attygalle, Jie Chen, Lila Dahal, Zhiquan Huang, Abdel-Rahman Ibdah, Prakash Koirala, Puja Pradhan, and Ambalanath Shan. RWC also acknowledges the motivating collaborations with research colleagues, Profs. Hiroyuki Fujiwara, Nikolas Podraza, and Sylvain Marsillac; Drs. Miklos Fried and Peter Petrik; as well as colleagues from the photovoltaics, glass, and instrumentation industries, Jeffrey Hale, Blaine Johs, Kenneth Kormanyos, Galen Pfeiffer, and David Strickler. Finally, RWC would like to thank Linda Collins for her continuous support. Gifu, Japan Toledo, USA

Hiroyuki Fujiwara Robert W. Collins

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Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hiroyuki Fujiwara 1.1 Photovoltaic Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Principles of Solar Cell . . . . . . . . . . . . . . . . . . . . 1.1.2 Sunlight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Performance of Various Solar Cells . . . . . . . . . . . 1.2 Optical Properties of Solar Cell Materials . . . . . . . . . . . . . . 1.2.1 Optical Constants and Dielectric Function . . . . . . 1.2.2 Optical Constants of Solar Cell Materials . . . . . . . 1.2.3 Dielectric Function Modeling . . . . . . . . . . . . . . . 1.3 Light Absorption in Solar Cells . . . . . . . . . . . . . . . . . . . . . 1.3.1 Light Absorption in Absorber Layer . . . . . . . . . . 1.3.2 EQE Characteristics . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Optical and Recombination Losses in Solar Cells . 1.4 Overview of This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 2 3 5 7 8 9 12 17 18 19 22 24 25

Analysis of Optical and Recombination Losses in Solar Cells . . . . Hiroyuki Fujiwara, Akihiro Nakane, Daisuke Murata, Hitoshi Tampo, Takuya Matsui and Hajime Shibata 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 ERS and ARC Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Optical Admittance Method . . . . . . . . . . . . . . . . . . 2.2.2 Treatment of Glass Substrate . . . . . . . . . . . . . . . . . . 2.2.3 Analysis of a Textured Solar Cell . . . . . . . . . . . . . . 2.3 e-ARC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Recombination Model . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Analysis of a CZTSe Solar Cell . . . . . . . . . . . . . . .

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29 35 36 41 43 50 50 53

Part I 2

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Application of Ellipsometry Technique

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2.3.3 Interpretation of EQE Spectra . . . . . . . . . EQE Analysis Examples . . . . . . . . . . . . . . . . . . . . 2.4.1 CZTSe and CZTS Solar Cells . . . . . . . . . 2.4.2 CdTe Solar Cell . . . . . . . . . . . . . . . . . . . 2.4.3 a-Si:H Solar Cell . . . . . . . . . . . . . . . . . . 2.5 EQE Analysis of Textured c-Si Solar Cells . . . . . . 2.5.1 Continuous Phase Approximation . . . . . . 2.5.2 Analysis of Flat c-Si Solar Cells . . . . . . . 2.5.3 Analysis of Textured c-Si Solar Cells . . . 2.6 Carrier Loss Mechanisms . . . . . . . . . . . . . . . . . . . 2.6.1 Effect of Carrier Collection Length on Jsc 2.6.2 Carrier Loss in Various Solar Cells . . . . . 2.7 Free Software for EQE Analysis . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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56 57 58 61 63 66 67 68 71 74 74 76 78 79

Optical Simulation of External Quantum Efficiency Spectra . . . . . Prakash Koirala, Abdel-Rahman A. Ibdah, Puruswottam Aryal, Puja Pradhan, Zhiquan Huang, Nikolas J. Podraza, Sylvain Marsillac and Robert W. Collins 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Hydrogenated Amorphous Silicon Solar Cells . . . . . . . . . . . . 3.2.1 Solar Cell Fabrication and Performance . . . . . . . . . . 3.2.2 Component Layer Dielectric Functions . . . . . . . . . . 3.2.3 Spectroscopic Ellipsometry Measurement and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 External Quantum Efficiency Simulations . . . . . . . . . 3.3 Cadmium Telluride Solar Cells . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Solar Cell Fabrication and Performance . . . . . . . . . . 3.3.2 Component Layer Dielectric Functions . . . . . . . . . . 3.3.3 Spectroscopic Ellipsometry Analysis . . . . . . . . . . . . 3.3.4 External Quantum Efficiency Simulations . . . . . . . . . 3.4 Copper Indium-Gallium Diselenide Solar Cells . . . . . . . . . . . . 3.4.1 Solar Cell Fabrication and Performance . . . . . . . . . . 3.4.2 Component Layer Dielectric Functions . . . . . . . . . . 3.4.3 Spectroscopic Ellipsometry Analysis . . . . . . . . . . . . 3.4.4 External Quantum Efficiency Simulations . . . . . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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84 85 85 87

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90 94 98 98 99 102 110 113 113 114 118 124 134 136

2.4

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Characterization of Textured Structures . . . . . . . . . . . . . . . . . . . . . 139 Hiroyuki Fujiwara and Yuichiro Sago 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 4.2 Characterization of Textured Structures in a-Si:H/c-Si Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Contents

4.2.1 Tilt-Angle SE Measurement . . . . . . . . . . . . . . . . 4.2.2 Analysis of Textured a-Si:H/c-Si Structures . . . . . 4.2.3 Effect of the Texture Size on a-Si:H Properties . . 4.2.4 Characterization of Textured Solar Cell Structures 4.3 Characterization of Textured Structures in Thin-Film Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 EMA Multilayer and Surface Area Models . . . . . 4.3.2 Analysis of a-Si:H Solar Cell Structures . . . . . . . 4.3.3 Analysis of lc-Si:H/a-Si:H Tandem Solar-Cell Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Analysis of CIGSe Solar Cell Structures . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

6

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143 144 146 149

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On-line Monitoring of Photovoltaics Production . . . . . . . . . . . . . Ambalanath Shan, Jie Chen, Prakash Koirala, Kenneth R. Kormanyos, Nikolas J. Podraza and Robert W. Collins 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 On-line Through-the-Glass SE for Rigid CdTe PV Panels in the Superstrate Configuration . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Equipment Design, Development, and Measurement Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Instrument Capabilities in Thin Film CdTe PV . . . . 5.3 On-Line SE for Roll-to-Roll Flexible PV in the Substrate Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Equipment Design, Development, and Measurement Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Applications in Thin Film a-Si:H PV . . . . . . . . . . 5.4 Summary and Future Directions . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Real Time Measurement, Monitoring, and Control of CuIn1−xGaxSe2 by Spectroscopic Ellipsometry . . . . . . . . . . . . . Puja Pradhan, Abdel-Rahman A. Ibdah, Puruswottam Aryal, Dinesh Attygalle, Nikolas J. Podraza, Sylvain Marsillac and Robert W. Collins 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Dielectric Functions Relevant for Real Time SE of CIGS . . 6.3 Real Time Measurement of Three-Stage Coevaporation of CIGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Deposition Details and Solar Cell Results . . . . . . 6.3.2 Standard CIGS Thickness in Continuous Process: Stage I (In1−xGax)2Se3 Deposition . . . . . . . . . . . . 6.3.3 Standard CIGS Thickness in Continuous Process: Stage II IGS Conversion to Cu-Rich CIGS . . . . .

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187 191 204 206

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6.3.4

Standard CIGS Thickness in Continuous Process: Stage II and III Transitions Between Cu-Rich CIGS and Cu-Poor CIGS . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Standard CIGS Thickness in Continuous Process: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.6 Standard CIGS Thickness in Shuttered Process: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.7 Thin CIGS in Shuttered Process: Summary . . . . . . 6.4 Issues in Real-Time Monitoring and Control . . . . . . . . . . . . 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

. . 234 . . 236 . . . . .

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Real Time and Mapping Spectroscopic Ellipsometry of Hydrogenated Amorphous and Nanocrystalline Si Solar Cells . . . . Zhiquan Huang, Lila R. Dahal, Sylvain Marsillac, Nikolas J. Podraza and Robert W. Collins 7.1 Introduction and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Real Time SE for Process Development: Nanocrystalline Si:H in p-i-n Tandem Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 General Strategy and Approaches . . . . . . . . . . . . . . . 7.2.2 Top Cell Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Dielectric Functions of Nanocrystalline Si:H n and p-Layers for the Tunnel Junction . . . . . . . . . . . . . . . . 7.2.4 Dielectric Functions of Bottom Cell Nanocrystalline Si:H i-Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.5 Real Time SE and Growth Evolution Diagram of nc-Si:H i-Layer Evolution . . . . . . . . . . . . . . . . . . . . . 7.2.6 Process-Performance Correlations for a-Si:H/nc-Si:H Tandem Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Mapping SE for Correlations with Device Performance: Optimization of nc-Si:H n-Layers in a-Si:H Solar Cells . . . . . . 7.3.1 General Strategy and Approaches . . . . . . . . . . . . . . . 7.3.2 Dielectric Function Determination for nc-Si:H n-Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Growth Evolution Diagram for nc-Si:H n-Layers . . . . 7.3.4 Mapping Spectroscopic Ellipsometry of Solar Cell Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.5 Property-Performance Correlations for Solar Cells . . . 7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

238 241 247 250 252 255

256 259 259 262 265 274 280 283 290 290 293 299 304 306 312 314

Contents

Part II 8

xiii

Optical Data of Solar-Cell Component Materials

Inorganic Semiconductors and Passivation Layers . . . . . . . . . . . Akihiro Nakane, Shohei Fujimoto, Gerald E. Jellison Jr., Craig M. Herzinger, James N. Hilfiker, Jian Li, Robert W. Collins, Takashi Koida, Shinho Kim, Hitoshi Tampo and Hiroyuki Fujiwara 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Optical Data of Inorganic Semiconductors and Passivation Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Ge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 SiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Al2O3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.5 Ga2O3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.6 SiN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.7 a-Si:H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.8 a-Si:H Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.9 a-SiC:H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.10 a-SiO:H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.11 lc-Si:H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.12 AlAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.13 GaAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.14 InAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.15 GaP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.16 InP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.17 AlSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.18 ZnS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.19 ZnSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.20 ZnTe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.21 CdS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.22 CdSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.23 CdTe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.24 CuInSe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.25 CuGaSe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.26 CuIn1−xGaxSe2 [Cu/(In + Ga) = 0.90] . . . . . . . . . . 8.2.27 CuInGaSe2-Based Compound [Cu/(In + Ga) = 0.69] . . . . . . . . . . . . . . . . . . . . . . 8.2.28 CuInGaSe2-Based Compound [Cu/(In + Ga) = 0.36] . 8.2.29 Cu2ZnSnS4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.30 Cu2ZnSnSe4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.31 Cu2ZnSn(SxSe1−x)4 . . . . . . . . . . . . . . . . . . . . . . . . 8.2.32 Cu2ZnGeSe4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.33 Cu2SnSe3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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322 322 325 328 329 331 332 338 340 346 350 354 356 358 360 363 365 367 369 370 372 374 376 378 380 382 384

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Contents

8.2.34 8.2.35 8.2.36 8.2.37 References . . . 9

In2S3 . MoS2 . MoSe2 MoSe2

.............. .............. (Polycrystal) . . . . (Single Crystal) . . ....................

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Organic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Takemasa Fujiseki, Shohei Fujimoto, Mariano Campoy-Quiles, Maria Isabel Alonso, Takurou N. Murakami, Tetsuhiko Miyadera and Hiroyuki Fujiwara 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Optical Data of Organic Semiconductors . . . . . . . . . . . . . . . 9.2.1 APFO-3 (F8TBT, PFDTBT) [Poly{2,7-(9,9Dioctylfluorene)-alt-5,5-(4’,7’-di-2-Thienyl-2’,1’,3’Benzothiadiazole)}] . . . . . . . . . . . . . . . . . . . . . . . 9.2.2 APFO-Green9 [Poly{2,7-(9,9-Dioctylfluorene)-alt5,5-(5,10-di-2-Thienyl-2,3,7,8-TetraphenylPyrazino-[2,3-g]Quinoxaline)}] . . . . . . . . . . . . . . . 9.2.3 Fluorinated CuPc (F16CuPc) [Fluorinated Copper Phthalocyanine] . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.4 MEH-PPV [Poly{2-Methoxy-5-(2’-EthylHexyloxy)-p-Phenylenevinylene}] . . . . . . . . . . . . . 9.2.5 P3HT [Poly(3-Hexylthiophene)] . . . . . . . . . . . . . . 9.2.6 P3HT:PC60BM (Blend Ratio 1:1) [Poly(3Hexylthiophene):(6,6)-Phenyl-C61-Butyric Acid Methyl Ester] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.7 P3HT:PC70BM (Blend Ratio 1:1) [Poly(3Hexylthiophene):(6,6)-Phenyl-C71-Butyric Acid Methyl Ester] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.8 P3OT [Poly(3-Octylthiophene)] . . . . . . . . . . . . . . . 9.2.9 PC60BM (Aka PCBM, [60]PCBM, PC61BM) [(6,6)-Phenyl-C61-Butyric Acid Methyl Ester] . . . . 9.2.10 PC70BM (Aka [70]PCBM, PC71BM) [(6,6)-Phenyl-C71-Butyric Acid Methyl Ester] . . . . 9.2.11 PCDTBT [Poly{N-9-Heptadecanyl-2,7-Carbazolealt-5,5-(4’,7’-di-2-Thienyl-2’,1’,3’Benzothiadiazole)}] . . . . . . . . . . . . . . . . . . . . . . . 9.2.12 PCPDTBT [Poly{2,6-(4,4-bis-(2-Ethylhexyl)-4HCyclopenta[2,1-b;3,4-b’]-Dithiophene)-alt-4,7(2,1,3-Benzothiadiazole)}] . . . . . . . . . . . . . . . . . . . 9.2.13 PEDOT:PSS [Poly(3,4-Ethylenedioxythiophene): Poly(4-Styrensulfonate)] . . . . . . . . . . . . . . . . . . . . 9.2.14 PMMA [Poly(Methyl Methacrylate)] . . . . . . . . . . .

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Contents

xv

9.2.15

9.2.16

9.2.17

9.2.18 9.2.19 9.2.20

PTB7 [Poly{[4,8-bis[(2-Ethylhexyl)Oxy] Benzo[1,2-b:4,5-b’]Dithiophene-2,6-Diyl] [3-Fluoro-2-[(2-Ethylhexyl)Carbonyl] Thieno[3,4-b]Thiophenediyl]}] . . . . . . . . . . . . . . . PTB7:PC70BM (Blend Ratio 1:1.5) [Poly{[4,8-bis [(2-Ethylhexyl)Oxy]Benzo [1,2-b:4,5-b’] Dithiophene-2,6-Diyl][3-Fluoro-2-[(2-Ethylhexyl) Carbonyl]Thieno[3,4-b]Thiophenediyl]}:(6,6)Phenyl-C71-Butyric Acid Methyl Ester] . . . . . . . . . Si-PCPDTBT [Poly{[4, 40-bis(2-Ethylhexyl) Dithieno(3,2-b:20,30-d)Silole]-2,6-Diyl-alt-[4,7-bis (2-Thienyl)-2,1,3-Benzothiadiazole]-5,50-Diyl}] . . . Spiro-OMeTAD [2,2’,7,7’-Tetrakis-(N, N-di-pMethoxyphenylamine) 9,9’-Spirobifluorene] . . . . . . TQ1 [Poly{2,3-bis-(3-Octyloxyphenyl)Quinoxaline5,8-Diyl-alt-Thiophene-2,5-Diyl}] . . . . . . . . . . . . . DPPTTT [Thieno(3,2-b)ThiopheneDiketopyrrolopyrrole] . . . . . . . . . . . . . . . . . . . . . .

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. . 467 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

10 Organic-Inorganic Hybrid Perovskites . . . . . . . . . . . . . . . . . . . . . Shohei Fujimoto, Takemasa Fujiseki, Masato Tamakoshi, Akihiro Nakane, Tetsuhiko Miyadera, Takeshi Sugita, Takurou N. Murakami, Masayuki Chikamatsu and Hiroyuki Fujiwara 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Optical Data of Hybrid Perovskites . . . . . . . . . . . . . . . . . . . . 10.2.1 FAPbI3 [HC(NH2)2PbI3] . . . . . . . . . . . . . . . . . . . . . 10.2.2 MAPbI3 (CH3NH3PbI3) . . . . . . . . . . . . . . . . . . . . . 10.2.3 MAPbBr3 (CH3NH3PbBr3) . . . . . . . . . . . . . . . . . . . 10.2.4 MAPb(I1-xBrx)3 [CH3NH3Pb(I1-xBrx)3] . . . . . . . . . . . 10.2.5 MAPbCl3 (CH3NH3PbCl3) . . . . . . . . . . . . . . . . . . . 10.2.6 FAPbI3 (d Phase) . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.7 PbI2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.8 CH3NH3I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Transparent Conductive Oxides . . . . . . . . . . . . . . . . . . . . . . . . . Akihiro Nakane, Shohei Fujimoto, Masato Tamakoshi, Takashi Koida, James N. Hilfiker, Gerald E. Jellison Jr., Takurou N. Murakami, Tetsuhiko Miyadera and Hiroyuki Fujiwara 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Optical Data of Transparent Conductive Oxides . . . . . . . . . . 11.2.1 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 In2O3 (Non-doped) . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

11.2.3 11.2.4 11.2.5 11.2.6 11.2.7 11.2.8 11.2.9 11.2.10 11.2.11 11.2.12 11.2.13 11.2.14 11.2.15 11.2.16 11.2.17 11.2.18 11.2.19 11.2.20 References . . .

In2O3:H (NHall = 2.1  1020 cm−3) . In2O3:Sn (NHall = 4.9  1020 cm−3) In2O3:Sn (NHall = 7.2  1020 cm−3) In2O3:Sn (NHall = 1.2  1021 cm−3) InZnO (NHall = 2.5  1020 cm−3) . . MoOx . . . . . . . . . . . . . . . . . . . . . . NiO . . . . . . . . . . . . . . . . . . . . . . . . SnO2 (Non-doped) . . . . . . . . . . . . . SnO2:F (TEC-15) . . . . . . . . . . . . . . TiO2 (Polycrystal) . . . . . . . . . . . . . TiO2 (Anatase Single Crystal) . . . . . TiO2 (Rutile Single Crystal) . . . . . . WO3 . . . . . . . . . . . . . . . . . . . . . . . ZnO (Non-doped) . . . . . . . . . . . . . . ZnO:Ga (NHall = 1.1  1020 cm−3) . ZnO:Al (Nopt = 1.5  1020 cm−3) . . ZnO:Ga (NHall = 4.8  1020 cm−3) . ZnO:Ga (NHall = 6.5  1020 cm−3) .

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12 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shohei Fujimoto, Takemasa Fujiseki and Hiroyuki Fujiwara 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Optical Properties and Reflectance of Metals . . . . . . . . 12.2.1 Optical Properties of Metals . . . . . . . . . . . . . 12.2.2 Reflectance at Semiconductor/Metal Interface . 12.3 Optical Data of Metals . . . . . . . . . . . . . . . . . . . . . . . . 12.3.1 Ag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Al . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.3 Au . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4 C (Graphite) . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5 Cr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6 Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.7 Mg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.8 Mo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.9 Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.10 Pt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.11 Ti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.12 W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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502 504 506 508 510 512 515 517 519 521 523 526 529 531 533 535 537 539 541

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Contents

13 Substrates and Coating Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . Shohei Fujimoto, Takemasa Fujiseki, James N. Hilfiker, Nina Hong, Mariano Campoy-Quiles and Hiroyuki Fujiwara 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Optical Data of Substrates and Coating Layers . . . . . . . . . . . . 13.2.1 SiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.2 Stainless Steel (SUS304) . . . . . . . . . . . . . . . . . . . . . 13.2.3 Polycarbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.4 PEN [Poly(Ethylene Naphthalate)] . . . . . . . . . . . . . . 13.2.5 PET [Poly(Ethylene Terephthalate)] . . . . . . . . . . . . . 13.2.6 PMMA [Poly(Methyl Methacrylate)] . . . . . . . . . . . . 13.2.7 Polyimide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.8 Kapton HN [Poly{N,N’-(Oxydiphenylene) Pyromellitimide}] . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.9 EVA [Ethylene Vinyl Acetate] . . . . . . . . . . . . . . . . 13.2.10 MgF2, LiF and NaF . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xvii

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

Contributors

Maria Isabel Alonso Institut de (ICMAB-CSIC), Bellaterra, Spain

Ciència

de

Materials

de

Barcelona

Puruswottam Aryal Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Dinesh Attygalle Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Mariano Campoy-Quiles Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Bellaterra, Spain Jie Chen Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Masayuki Chikamatsu Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Robert W. Collins Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Lila R. Dahal Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Shohei Fujimoto Gifu University, Gifu, Japan Takemasa Fujiseki Gifu University, Gifu, Japan Hiroyuki Fujiwara Gifu University, Gifu, Japan Craig M. Herzinger J.A. Woollam Co., Inc., Lincoln, NE, USA James N. Hilfiker J.A. Woollam Co., Inc., Lincoln, NE, USA

xix

xx

Contributors

Nina Hong J.A. Woollam Co., Inc., Lincoln, NE, USA Zhiquan Huang Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Abdel-Rahman A. Ibdah Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Gerald E. Jellison Jr. Oak Ridge National Laboratory, Oak Ridge, TN, USA Shinho Kim Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Takashi Koida Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Prakash Koirala Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Kenneth R. Kormanyos Calyxo USA, Perrysburg, OH, USA Jian Li University of Toledo, Toledo, OH, USA Sylvain Marsillac Virginia Institute of Photovoltaics, Old Dominion University, Norfolk, VA, USA Takuya Matsui Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Tetsuhiko Miyadera Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Takurou N. Murakami Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Daisuke Murata Gifu University, Gifu, Japan Akihiro Nakane Gifu University, Gifu, Japan Nikolas J. Podraza Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Puja Pradhan Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA Yuichiro Sago Gifu University, Gifu, Japan Ambalanath Shan Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH, USA

Contributors

xxi

Hajime Shibata Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Takeshi Sugita Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Masato Tamakoshi Gifu University, Gifu, Japan Hitoshi Tampo Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan

Chapter 1

Introduction Hiroyuki Fujiwara

Abstract From optical constants (refractive index n and extinction coefficient k) extracted from ellipsometry technique, advanced optical analyses, including current loss analyses and structural analyses of textured devices, can be performed. The optical response in solar cell devices is essentially governed by the optical constants of solar-cell component layers and detailed optical analysis/simulation is of significant importance in maximizing conversion efficiencies. In this chapter, I review the operating principles of practical solar cells particularly based on the view of the absorber optical properties. Specifically, the relationship between solar cell characteristics and absorber absorption properties is discussed. The critical need of the optical and recombination loss analysis based on external quantum efficiency characterization is emphasized. By comparing the absorption spectra of various solar cell materials, the optical properties of semiconductors are further discussed. This chapter will also provide an overview for the contents of subsequent chapters in this book.

1.1

Photovoltaic Devices

A solar cell is basically a simple p-n junction device and its operation is quite straightforward. However, a complex device structure is often required to minimize the power loss induced by light reflection, unfavorable parasitic absorption and carrier recombination. To understand such power loss mechanisms in the devices, accurate knowledge for optical processes in solar cells are necessary. In this section, the characteristics of various solar cells are summarized in terms of absorber (semiconductor) optical properties.

H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_1

1

2

1.1.1

H. Fujiwara

Principles of Solar Cell

Figure 1.1 shows (a) a simplified structure of a p-n junction solar cell with a transparent conductive oxide (TCO) front electrode and (b) the absorption coefficient (α) spectrum of CuInSe2 (CISe) [1]. In Fig. 1.1a, the p layer is absorber and the photocarriers are generated within the semiconducting absorber layer under light illumination. In this case, the short-circuit current density (Jsc) is generated in the short-circuit condition, whereas the open-circuit voltage (Voc) is obtained in the open-circuit condition. By using the fill factor (FF), the conversion efficiency is determined as

 ηð%Þ = Jsc A ̸ cm2 × Voc ðVÞ × FF ð%Þ ̸0.1 W ̸ cm2

ð1:1Þ

For most of solar cells, FF values are 70–80% [2]. In other words, the power output is governed primarily by Jsc and Voc (i.e., P ∝ Jsc × Voc ). In Fig. 1.1b, the α value of CISe increases rapidly near the band gap (Eg = 1.00 eV), followed by a gradual increase above Eg. In general, Voc increases with Eg, while Jsc is determined essentially by the product of αd, where d is the thickness of the absorber layer (Sect. 1.3). Thus, the two important parameters of solar cells (Voc and Jsc) can be deduced from the α spectrum of the absorber. In other words, the ultimate potential of solar cell materials can be judged from the α spectrum alone, and accurate determination of absorber optical properties is therefore of significant importance. Figure 1.2 shows more detailed optical and physical processes in a solar cell. In this figure, a hypothetical band diagram for a TCO layer/doped layer (n)/absorber (p)/metal structure is indicated. Under sunlight illumination, the reflection loss

Fig. 1.1 a Structure of a p-n junction solar cell consisting of TCO/n layer/p layer/metal and b α spectrum of CISe [1]. The complete optical data of CISe are shown in Fig. 8.24

1 Introduction

3

Fig. 1.2 Optical and physical processes in a solar cell with a structure of TCO/n layer/p layer/ metal. The hypothetical band diagram is shown. The current losses in solar cells can be categorized into reflection, absorption and recombination losses

generally occurs by the front- and back-side reflections (see also Fig. 2.2). Some of the sunlight is absorbed in TCO, doped and metal layers, which causes the unfavorable absorption loss in the solar cell. In Fig. 1.2, the light absorption in the semiconducting p layer generates photocarriers, but some of the photocarriers recombine at defect states created within the bulk layer or at the front and rear interfaces, which constitutes the recombination loss. For the development of high-efficiency solar cells, it is necessary to minimize reflection, parasitic absorption and recombination losses. It should be emphasized that all of these losses can be determined quantitatively from detailed external quantum efficiency (EQE) analyses (Fig. 1.14 and Chap. 2).

1.1.2

Sunlight

In general, for the calculation of Jsc, a standard air-mass 1.5 global (AM1.5G) spectrum is used as the sunlight spectrum. Here, the “global” for AM1.5 implies that the component of scattered (diffused) light is included. Figure 1.3 shows the spectral irradiance of AM1.5G versus (a) wavelength and (b) photon energy, together with the spectral photon density of AM1.5G versus (c) wavelength and (d) photon energy. The numerical values are taken from [3]. Note that the irradiance is defined as watts per meter squared (W/m2), whereas more conventional light intensity is defined differently as the power per unit solid angle from a point source. In Fig. 1.3, sharp drops observed in the irradiance and photon density originate from the light absorption induced by O3, O2, H2O and CO2 in the atmosphere. Although the sunlight spectrum is generally represented by Fig. 1.3a, this spectrum

4

H. Fujiwara

Fig. 1.3 Spectral irradiance of sunlight (AM1.5G) versus a wavelength and b photon energy, together with the spectral photon density of AM1.5G versus c wavelength and d photon energy. The numerical data are taken from [3]. The Jsc of solar cells is calculated from these spectra

does not correlate with actual photocarrier density generated under the sunlight illumination, as the irradiance becomes higher when the energy of photon is high. More specifically, the photon energy E is calculated from the wavelength λ by E = hc ̸ λ,

ð1:2Þ

where h and c show Planck’s constant (h = 6.62607 × 10−34 J s) and the speed of light (c = 2.99792 × 108 m/s), respectively. If electron-volt unit is used (1 eV = 1.60218 × 10−19 J), we obtain E=

1 hc 1239.8 = eV. ⋅ 1.60218 × 10 − 19 λ λðnmÞ

ð1:3Þ

1 Introduction

5

By employing (1.2), the spectral photon density per second per meter squared is calculated as ρphoton ðλÞ =

FðλÞ λ = FðλÞ , E hc

ð1:4Þ

where F(λ) represents the spectral irradiance shown in Fig. 1.3a. The result calculated from (1.4) has been shown in Fig. 1.3c. The ρphoton versus E, obtained from a similar calculation, is also indicated in Fig. 1.3d. It can be seen that ρphoton shows a maximum at 0.8 eV, while ρphoton is quite low in a high energy region (E > 3 eV). Accordingly, the effect of the light absorption in the high-E region is negligible in solar cells. From ρphoton, the current density is then determined as J = qρphoton ,

ð1:5Þ

where q shows the electron charge (q = 1.60218 × 10−19 C). If the maximum ρphoton of 4 × 1021 s−1m−2eV−1 with a width of 2 eV is assumed for the spectrum of Fig. 1.3d, the upper limit of Jsc can be approximated by Jsc = ð1.60218 × 10 − 19 Þ ⋅

ð4 × 1021 Þ × 2 ⋅ 10 − 4 ∼ 0.064 A ̸cm2 . 2

ð1:6Þ

Thus, if all the sunlight (E > 0.3 eV) is converted to the photocurrent, we roughly obtain 64 mA/cm2.

1.1.3

Performance of Various Solar Cells

In solar cells, photocarriers are generated when the energy of photons is higher than Eg, although the light absorption still occurs even below Eg due to the presence of tail-state absorption. If the light absorption in the absorber layer is assumed to occur only above Eg, the maximum Jsc is calculated according to the following equation using (1.5): Z∞ ρphoton ðEÞdE.

Jsc, max = q

ð1:7Þ

Eg

In the above equation, ρphoton(E) corresponds to the spectrum of Fig. 1.3d. Figure 1.4a shows the calculated Jsc,max as a function of Eg, together with reported Jsc values of actual solar cells. The experimental Jsc data are taken from [2], except for CdTe [4], Cu(In,Ga)Se2 (CIGSe) [5], Cu2ZnSnSe4 (CZTSe) [6], Cu2ZnSnS4 (CZTS) [7], Cu2ZnSn(S,Se)4 (CZTSSe) [8], Cu2Zn(Sn,Ge)Se4 (CZTGSe) [9], CH3NH3PbI3 (MAPbI3) [10], and HC(NH2)2PbI3 (FAPbI3) [11].

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Fig. 1.4 a Maximum Jsc (Jsc,max) calculated from (1.7) as a function of Eg and b difference between Jsc,max and experimental Jsc (ΔJsc = Jsc,max − Jsc). The experimental Jsc values are taken from [2], except for CdTe [4], Cu(In,Ga)Se2 (CIGSe) [5], Cu2ZnSnSe4 (CZTSe) [6], Cu2ZnSnS4 (CZTS) [7], Cu2ZnSn(S,Se)4 (CZTSSe) [8], Cu2Zn(Sn,Ge)Se4 (CZTGSe) [9], CH3NH3PbI3 (MAPbI3) [10], and HC(NH2)2PbI3 (FAPbI3) [11]

The Eg values of the CZTSe, CZTS and CZTSSe were extracted from the EQE analyses [12]. In Fig. 1.4a, the experimental Jsc follows the trend of Jsc,max and decreases with increasing Eg as the integrated ρphoton becomes smaller. In some solar cells, however, Jsc is much smaller than Jsc,max and the difference between Jsc,max and Jsc (i.e., ΔJsc = Jsc,max − Jsc) represents the optical and recombination losses. Figure 1.4b shows ΔJsc as a function of Eg, calculated from the result of Fig. 1.4a. As confirmed from this result, the crystalline Si (c-Si), GaAs, CdTe and CH3NH3PbI3 solar cells show very small ΔJsc of ∼2 mA/cm2. In fact, quite high conversion efficiencies (18–29%) have been confirmed for these solar cells [2, 4, 10]. On the other hand, even though the CIGSe solar cell has a high efficiency of 21.7%, ΔJsc of this solar cell is rather large (6.6 mA/cm2). This is due to the strong parasitic absorption in TCO (ZnO:Al), CdS and Mo layers (Fig. 2.11). It should be noted that the ΔJsc values of the CZTSe, CZTS and CZTSSe solar cells are underestimated as these solar cells exhibit relatively large tail absorption below Eg and the actual current loss is larger. The result of Fig. 1.4b shows clearly that the suppression of the Jsc loss is quite important to achieve high conversion efficiencies. As mentioned above, Voc shows a strong correlation with Eg. If we assume Voc loss (Vloss) in solar cells, we can express Voc as Voc =

Eg − Vloss . q

ð1:8Þ

1 Introduction

7

Fig. 1.5 Calculated conversion efficiency as a function of Eg, together with the experimental efficiencies of the solar cells shown in Fig. 1.4. The efficiency curves were calculated by changing Vloss in (1.8) in a range from 0.3 to 0.6 V assuming FF = 0.85

In this case, the conversion efficiency can be calculated from (1.1) by further assuming a constant FF value. Figure 1.5 shows the calculated conversion efficiency as a function of Eg, together with the experimental efficiencies of the solar cells. For the calculation, FF = 0.85 was assumed and several efficiency curves were calculated by changing Vloss in a range from 0.3 to 0.6 V. For the GaAs solar cell, FF is quite high (86.5%) and Vloss is quite low (0.30 V). As a result, the experimental efficiency of the GaAs solar cell is quite close to the calculation limit of Vloss = 0.3 V. In Fig. 1.5, the maximum efficiency is obtained at 1.4 eV for Vloss ≥ 0.4 V, while the conversion efficiencies show high values in a range of Eg = 1.1–1.4 eV if Vloss = 0.3 V. It can be seen that, for most of the solar cells, the conversion efficiencies are much smaller than the calculated values. In particular, for thin-film solar cells, which have been developed mainly to realize low-cost solar cells, the overall efficiencies are quite low. Accordingly, for these solar cells, the analysis of power loss mechanism and the following optimization of solar cell structures and processing are crucial.

1.2

Optical Properties of Solar Cell Materials

As discussed in Fig. 1.1, the conversion efficiency of solar cells is ultimately governed by the absorption characteristics of solar-cell absorber layers. Thus, the understanding of the absorption properties is of utmost importance. In this section, the basic ideas of optical constants (or dielectric function) are addressed. This section will further provide the comparison of optical spectra obtained from various solar cell materials.

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H. Fujiwara

Optical Constants and Dielectric Function

The propagation of light (electromagnetic wave) in media is expressed completely by refractive index n and extinction coefficient k (Chap. 1 (Vol. 1)). In optics, the values of (n, k) are combined to yield a single complex number and we define complex refractive index N by N ≡ n − ik.

ð1:9Þ

The absolute value of N is determined from a complex dielectric constant defined by ε ≡ ε1 − iε2

ð1:10Þ

and, by Maxwell’s equations, N is expressed from ε as follows [13]: N 2 ≡ ε.

ð1:11Þ

ε1 = n 2 − k 2 ,

ð1:12Þ

ε2 = 2nk.

ð1:13Þ

From the above equations, we get

The variation of ε with E is generally referred to as dielectric function. The ε1 spectrum basically shows the refractive index component, whereas the ε2 spectrum essentially shows the light absorption characteristic as the magnitude of k represents the light absorption strength. In fact, when k = 0, we obtain ε2 = 0 (ε1 = n2) from (1.12) and (1.13). On the other hand, from (ε1, ε2), (n, k) can also be calculated: n=

nh
1 ̸ 2 i o 1 ̸ 2 ε1 + ε21 + ε22 , ̸2

nh k=


1 ̸2 i o1 ̸2 − ε1 + ε21 + ε22 . ̸2

ð1:14Þ ð1:15Þ

From k, absorption coefficient can further be obtained as α=

4πk . λ

ð1:16Þ

The above equation shows an important relation between k and α. When there is no light absorption, it follows that α = k = ε2 = 0. If the unit of λ is nm, α with a conventional unit of cm−1 is calculated by

1 Introduction

9

αðcm − 1 Þ =

1.2.2

4πk 4πk ⋅ EðeVÞ ⋅ 107 = ⋅ 107 . λðnmÞ 1239.8ðnmÞ

ð1:17Þ

Optical Constants of Solar Cell Materials

Figure 1.6 summarizes the α spectra of various solar cell materials versus (a) E and (b) λ. The complete optical data of these materials can be found in Chaps. 8 and 10. In the figure, the Eg positions of each material are indicated by the closed circles. For a high efficiency CIGSe solar cell [5], the alloy composition of CuIn0.8Ga0.2Se2 was employed and the corresponding spectrum calculated from the CIGSe optical database (Sect. 10.4 (Vol. 1)) is shown. It can be seen that many direct-transition semiconductors show similar α values of ∼104 cm−1 and, at the exact Eg positions, the α values are around 5 × 103 cm−1. In contrast, the indirect-transition semiconductors, including Si, Ge, GaP and AlAs, exhibit much lower values of α = 2–24 cm−1 at the Eg positions. Although GaP is an indirect transition semiconductor, GaInP alloys, for example, show the direct transition in a broad compositional range [14] and have been applied to concentrator/space solar cells (Chap. 14 (Vol. 1)). Except for c-Si and microcrystalline Si [15], no other indirect transition semiconductors have been investigated intensively for solar cell application due to low α values. For multi-junction devices, however, Ge substrates have been employed to widen the spectral response [16]. The hydrogenated amorphous silicon (a-Si:H) is generally considered to have a pseudo-direct band gap by zone folding [17], but α of a-Si:H at the Eg position of 1.65 eV is rather small (∼100 cm−1). In earlier studies, high conversion efficiencies of CH3NH3PbI3 solar cells were attributed to very large α values [18, 19]. However, the α values of the hybrid perovskite have been overestimated seriously (see Chap. 6 (Vol. 1)) and the actual α values are comparable to those of other direct-transition semiconductors. Detailed EQE analysis shows that high Jsc observed in CH3NH3PbI3 solar cells is caused by very low parasitic absorption in the solar cells (Sect. 16.3 (Vol. 1)). Thus, solar cell structures also affect the resulting performance significantly. As shown in Fig. 1.6, kesterite semiconductors such as CZTSe and CZTS exhibit quite large tail-state absorption and the relatively large α values are observed even below Eg [12]. The presence of the absorption tail can be confirmed more easily when α is plotted versus λ. The a-Si:H layers also show strong tail absorption due to disordered amorphous network structures [20]. In general, to characterize the tail-state absorption, the Urbach energy EU, defined by α = α0 expðE ̸EU Þ (i.e., ln α ∝ E ̸ EU ), is estimated. Figure 1.7a shows EU of various semiconductors as a function of Eg. The EU values were obtained from the α spectra of Fig. 1.6 in the region below Eg. In this simple analysis, however, slight ambiguity remains due to the deviation from the assumed exponential variation. In Fig. 1.7a, EU of single crystals, denoted by the open circles, shows a low value

10

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1 Introduction

11

◀Fig. 1.6 α spectra of various solar cell materials versus a photon energy and b wavelength. The

complete optical data of these materials are shown in Chaps. 8 and 10. The closed circles indicate the Eg positions of each absorber material. For high efficiency Cu(In,Ga)Se2 solar cells, the composition of CuIn0.8Ga0.2Se2 has been used and the corresponding spectrum is shown. It should be noted that the optical constants of a-Si:H are process dependent (Sect. 9.4 (Vol. 1))

of ∼9 meV, except for Ge. The polycrystalline materials, including CIGSe, CdTe and hybrid perovskites, also show very sharp absorption edges with small EU of ∼15 meV (closed circles in Fig. 1.7a). In contrast, for the CZTSe and CZTS, large EU values of ∼70 meV have been obtained, although these EU values vary depending on the analyzed energy region. In Fig. 1.7a, the EU values for direct and indirect semiconductors are shown, but EU of the indirect materials (Si and Ge) could not be compared directly with those of the direct-transition absorbers. The presence of the tail states is detrimental for solar cells and increases Vloss in (1.8). Figure 1.7b summarizes Vloss obtained from the solar cells of Fig. 1.4 as a function of EU. The Vloss values were calculated from (1.8) using the experimental Voc and Eg values. It can be seen that Vloss increases significantly with increasing EU, as pointed out previously [21]. Unfortunately, the interpretation of Vloss is not straightforward and Vloss is also affected by carrier recombination and built-in potential. Thus, the data points of Fig. 1.7b scatter notably. However, the result of Fig. 1.7b implies that small EU is quite important to suppress Vloss in solar cells. On the other hand, when the α values near Eg are higher, the light absorption occurs more close to the front interface, and the effect of the rear-interface recombination becomes smaller (Sect. 2.6). Accordingly, the band-edge absorption characteristics directly affect the solar cell performance. For solar cell application, it is preferable if a light absorber has (i) the optimum Eg value of ∼1.4 eV (Fig. 1.5),

Fig. 1.7 a EU determined from the α spectra of Fig. 1.6 as a function of Eg and b Vloss obtained for the solar cells of Fig. 1.4 as a function of EU. The open circles show the EU values of single crystalline semiconductors, whereas the closed circles indicate those extracted from polycrystalline materials. The closed square shows the value of the a-Si:H

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H. Fujiwara

(ii) a low Urbach energy (Fig. 1.7b) and (iii) high α values near Eg [12]. Among the existing solar-cell materials, GaAs, InP, CdTe and CH3NH3PbI3 semiconductors fulfill these conditions relatively well. Figure 1.8 shows (a) the ε2 spectra and (b) the k spectra of various solar cell materials. These optical data are consistent with those of Fig. 1.6. The ε2 values near Eg are ∼0.5 for the direct-transition semiconductors, while the indirect semiconductors show almost zero ε2 values near Eg. The corresponding k values of the direct semiconductors are ∼0.1, whereas those of the indirect semiconductors are also almost zero.

1.2.3

Dielectric Function Modeling

The dielectric functions (or optical constants) modeled using theoretical expressions are particularly useful for ellipsometry analyses and optical simulations, as tabulated data have a limited number of data points. In this book, therefore, the optical data of 148 solar-cell component materials have been parameterized completely. All the model parameters and the tabulated optical data are summarized in Part II. Quite importantly, it is established in this book that the dielectric function modeling of all the solar-cell component materials can be performed using only three models: i.e., (i) the Sellmeier model, (ii) the Tauc-Lorentz (TL) model [22], and (iii) the Drude model. Figure 1.9 summarizes the overall shapes of the dielectric functions calculated from (a) the Sellmeier, (b) TL and (c) Drude models. In general, the Sellmeier model is applied for the modeling of transparent materials and insulators, such as SiO2 and Al2O3 (see Chap. 8). In this model, the light absorption in the material is assumed to be zero (i.e., ε2 = k = 0) and ε1 is calculated by εSel ðλÞ = ε1 ðλÞ = n2 ðλÞ =


B 1 λ2 B λ2 B λ2  +
2 2  +
2 3  +1 λ − C1 λ − C2 λ − C3 2

ð1:18Þ

In this model, there are a total of six parameters (B1, B2, B3, C1, C2, C3) and the n spectrum can be calculated quite easily from these parameter values (see also Chap. 5 (Vol. 1)). In the TL model [22], the dielectric function is calculated using five free parameters: the ε1 value at high energy [ε1(∞)], the amplitude (A), width (C), band gap (Eg) and peak position (E0) of the ε2 peak (see Fig. 1.9b). Using these parameters, the ε2 peak (spectrum) is calculated as ε2 ðEÞ =

ACE0 ðE − Eg Þ2 ðE2

− E02 Þ2

+ C2 E2

⋅


 1
E > Eg , ε2 ðEÞ = 0 E ≤ Eg E

ð1:19Þ

1 Introduction

13

Fig. 1.8 a ε2 spectra and b k spectra of various solar cell materials. The optical data are consistent with those shown in Fig. 1.6. The ε2 spectra are shown for photon energy, while the k spectra are indicated for wavelength

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Fig. 1.9 Dielectric function models of a the Sellmeier model, b the Tauc-Lorentz (TL) model, and c the Drude model, which are employed for the dielectric function modeling of transparent, semiconductor, and metal (TCO) materials, respectively. The TL model is expressed by a total of five parameters: the amplitude parameter (A), broadening parameter (C), Tauc optical gap (Eg), peak transition energy (E0), and energy-independent contribution to ε1(E) [ε1(∞)], whereas the Drude model is expressed by the amplitude parameter (AD) and the broadening parameter (Γ). In b, ε∞ represents the high-frequency dielectric constant and is not a model parameter

1 Introduction

15

The corresponding ε1(E) can be obtained based on the Kramers-Kronig relations: ! E02 + Eg2 + αEg AC aln ε1 ðEÞ = ε1 ð∞Þ + 4 ⋅ ln 2 E0 + Eg2 − αEg πξ 2αE0      A aatan − 1 2Eg + α − 1 − 2Eg + α − 4⋅ π − tan + tan C C E0 πξ " !# 2 2 γ − Eg AE0 + 2 4 Eg ðE2 − γ 2 Þ π + 2 tan − 1 2 αC πξ α 2 3     2 2     E + E E − Eg AE0 C 2AE0 C g 6 E − Eg ðE + Eg Þ 7 ln ⋅ Eg ln4qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5 − + E + Eg E πξ4 πξ4 ðE02 − Eg2 Þ2 + Eg2 C 2 ð1:20Þ where aln = ðEg2 − E02 ÞE2 + Eg2 C2 − E02 ðE02 + 3Eg2 Þ,

ð1:21Þ

aatan = ðE 2 − E02 ÞðE02 + Eg2 Þ + Eg2 C 2 ,

ð1:22Þ

ξ4 = ðE 2 − γ 2 Þ2 + α2 C2 ̸4,

ð1:23Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4E02 − C 2 ,

ð1:24Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E02 − C2 ̸2.

ð1:25Þ

α= γ=

Although the above equations are rather complicated, the dielectric function of the TL model can be calculated rather easily using five parameters (A, C, Eg, E0, ε1(∞)). For example, the dielectric function of an a-Si:H layer deposited at 230 °C has been parameterized assuming a single TL peak with parameter values of A = 214.05 eV, C = 2.33 eV, E0 = 3.649 eV, Eg = 1.659 eV and ε1(∞) = 0.309 (see Table 8.19). If E = 2 eV, using these parameter values, we obtain ε2 = 0.98 directly from (1.19). For the ε1 value, we get aln = −314.55, aatan = −134.73, ξ4 = 108.49, α = 6.92, γ = 3.26 from the assumed TL parameters using (1.21)– (1.25). With these values, (1.20) becomes ε1 = ε1 ð∞Þ − 9.11 lnð6.01Þ + 23.19½π − tan − 1 ð4.39Þ + tan − 1 ð1.55Þ

 − 7.28 π + 2 tan − 1 ð0.98Þ − 18.03 lnð0.09Þ + 17.72 lnð0.11Þ = 0.31 − 16.34 + 64.76 − 34.16 + 43.42 − 39.11 = 18.88

ð1:26Þ

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H. Fujiwara

As a result, ε of a-Si:H at 2.0 eV is calculated to be ε = 18.88 − i0.98. For the ε1(E) calculation, however, E should be chosen so that |E − Eg| in (1.20) does not become zero. The Drude model shown in Fig. 1.9c is an important model, which has been employed extensively to express light absorption by free electrons (i.e., free carrier absorption) in TCO and metal materials. When the carrier concentration is high (typically >1018 cm−3), the ε1 value becomes negative and ε2 shows a large increase at lower energy. The theoretical expression of the Drude model is simple and is given by εD ðEÞ = −

AD = E 2 − iΓE

 −

   AD AD Γ − i , E 3 + Γ2 E E2 + Γ2

ð1:27Þ

where AD and Γ are the amplitude and broadening parameters, respectively. From these two parameters, carrier concentration and carrier mobility can further be obtained (Chap. 18 (Vol. 1)). In this book, the dielectric functions of the inorganic (Chap. 8), organic (Chap. 9) and hybrid perovskite (Chap. 10) semiconductors are modeled simply by combining several TL ε2 peaks and the corresponding ε1(E) is also calculated as a sum of the ε1 contributions obtained from each TL peak. On the other hand, the dielectric functions of TCO materials (Chap. 11) and metals (Chap. 12) have been modeled by combining the TL model with the Drude model. Figure 1.10 shows the examples of the dielectric function modeling performed for an indirect-transition semiconductor (c-Si), a direct-transition semiconductor (CISe), an organic semiconductor (P3HT) and a TCO (ZnO:Ga). The open circles indicate the experimental data shown in Fig. 8.1 (c-Si), Fig. 8.24 (CISe), Fig. 9.5 (P3HT) and Fig. 11.20 (ZnO:Ga), and the solid lines show the fitting results. The individual peak in Fig. 1.10 shows the TL peak and the sum of these peaks provides excellent agreement with the experimental data. In the parameterization of inorganic semiconductors, α spectra in the logarithmic scale are reproduced almost perfectly through careful modeling (Chap. 8). In the dielectric function modeling of TCO, free carrier absorption observed at low energies (E < 3 eV) was incorporated using the Drude model (Chaps. 5 and 18 in Vol. 1). As confirmed from Fig. 1.10, the optical spectra of the indirect, direct and organic semiconductors are quite different. As mentioned above, near Eg, ε2 ∼0 in the indirect semiconductor, while the sharp onset of light absorption is observed in the direct CISe semiconductor. The aromatic polymer materials often exhibit sharp absorption peaks in the visible region, characterized by π → π* transition (Chaps. 4 and 15 in Vol. 1). The ε2 shape of the TCO can be interpreted as a sum of the TL and Drude models shown in Fig. 1.9. The free carrier absorption in TCO layers increases with free carrier concentration (Chap. 18 (Vol. 1)) and the optimization of the TCO carrier concentration is important in solar cell devices (Chap. 2).

1 Introduction

17

Fig. 1.10 Results of dielectric function modeling performed for Si (indirect transition), CISe (direct transition), P3HT (organic compound) and ZnO:Ga (TCO). The open circles indicate the experimental data shown in Fig. 8.1 (Si), Fig. 8.24 (CISe) [1], Fig. 9.5 (P3HT) and Fig. 11.20 (ZnO:Ga), whereas the solid lines represent the parameterization results. For P3HT, the chemical structure of the polymer is shown. The individual peaks show the TL peaks and the red lines show the sum of these peaks. For the modeling of the ZnO:Ga, the Drude model has been incorporated to express the free carrier absorption

1.3

Light Absorption in Solar Cells

The photocarrier generation by light absorption is an essential process in the operation of solar cells. The light absorption phenomena in experimental solar cells can be studied systematically based on EQE analyses. In particular, a global EQE analysis method has been established, from which all the current losses (i.e., reflection, absorption and recombination losses in Fig. 1.2) can be estimated rather easily (Chap. 2). In this section, the light absorption in photovoltaic devices is explained more quantitatively and the examples of EQE analyses performed for the state-of-the-art CIGSe and CZTSSe solar cells are introduced briefly.

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H. Fujiwara

Light Absorption in Absorber Layer

When samples consist of only substrates with infinite thickness, light absorption in the samples can be expressed by Beer’s law [13]: I = I 0 expð − αdÞ,

ð1:28Þ

where I shows the light intensity along the sample depth d and I0 indicates the light intensity at the material surface. Figure 1.11a shows the light intensity ratio (I/I0) versus the depth from the surface (i.e., d), calculated from (1.28). In the figure, the calculation results for α = 104 and 105 cm−1 are shown. As confirmed from Fig. 1.11a, I/I0 decreases along d due to the light absorption, and the decay of the light intensity is more pronounced at high α because of stronger light absorption. The gray area indicated in Fig. 1.11a shows the actual light absorption in the sample, which can be expressed simply as L = 1 − expð − αdÞ.

ð1:29Þ

Accordingly, the extent of light absorption in media is determined by the αd product. On the other hand, when I/I0 = 1/e ∼ 37% in (1.28), we obtain αd = 1. This depth defines the penetration depth of light (dp), which is given by dp ≡ 1 ̸ α .

ð1:30Þ

Fig. 1.11 a Light intensity ratio (I/I0) versus the depth from the surface d, calculated from I/I0 = exp(−αd) and b penetration depth of light (dp) versus α, determined from dp = 1/α. In a, the calculation results for α = 104 and 105 cm−1 are shown and the depth at I/I0 = 1/e ∼ 37% defines dp. The contribution of light absorption is indicated by the gray region in a. In b, the dp values for α = 102 cm−1 (c-Si) and 104 cm−1 (CIGSe) are indicated by the arrows

1 Introduction

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Figure 1.11b shows p calculated from (1.30) as a function of α. Since dp is idnversely proportional to α, the dp value decreases rapidly with increasing α. This shows a well-known fact that the light absorption occurs more close to the surface when α is higher. As confirmed from Fig. 1.6, α of c-Si at the energy slightly above Eg is ∼100 cm−1. This α corresponds to dp of 100 μm, as indicated by the arrow in Fig. 1.11b. In many direct-transition semiconductor (i.e., CIGSe, GaAs, CdTe, etc.), α above Eg is ∼104 cm−1, which is equivalent to dp ∼1 μm. These dp values are quite consistent with the thicknesses of the absorber layers employed in the actual solar cells. Thus, high α is vital to achieve sufficient optical absorption with a limited absorber thickness. In the above calculation, however, the infinite absorber thickness was assumed and the influence of the back-side reflection was neglected completely. The effective back-side reflection and higher optical confinement become particularly important when the thickness of the light absorbers cannot be increased due to a process limitation (spin coating, etc.) or a physical reason (high defect density, etc.). For CH3NH3PbI3 and a-Si:H solar cells with absorber thicknesses of 200–300 nm, therefore, the high reflectivity at the rear interface is critical (see also Fig. 12.3). Since α changes depending on λ (or E), dp also varies with λ. By taking advantage of the λ-dependent dp, the carrier recombinations that occur at the front and rear interfaces can be distinguished (see Fig. 2.17). It should be noted that dp merely shows the position where the normalized light intensity becomes 37% (see Fig. 1.11a). Thus, the weaker light absorption continues to occur in the deeper region.

1.3.2

EQE Characteristics

The quantitative assessment of light absorption in solar cells can be made from EQE characterization. Here, we discuss the relation between the light absorption and the resulting EQE response observed in various solar cells. Figure 1.12 shows (a) αd spectra of various light absorbers and (b) EQE spectra of solar cells. As we have seen in Fig. 1.11a, the light absorption in the absorber is expressed by αd. For the calculation of αd in Fig. 1.12a, the α spectra of Fig. 1.6 and the absorber thicknesses employed for the corresponding solar cells in Fig. 1.12b were employed. The EQE spectra in Fig. 1.12b show those reported for a-SiO:H/c-Si heterojunction [23] (Fig. 2.26), CIGSe [24] (Fig. 2.9), CdTe [25] (Fig. 2.21), a-Si:H (Fig. 2.23) and CH3NH3PbI3 [26] (Fig. 16.17c in Vol. 1) solar cells. The absorber thicknesses of these solar cells were indicated in Fig. 1.12a. Although c-Si is an indirect semiconductor with low α values, the absorber thickness (typically ∼150 μm) is sufficient and the αd values are comparable to those of CIGSe and CdTe. In contrast, the a-Si:H and CH3NH3PbI3 show smaller αd due to thin thicknesses (200–300 nm). The dotted lines for the EQE spectra indicate the results of liner fitting analyses performed in the Eg region and the λ positions of the intercepts are denoted by the orange arrows. The identical

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Fig. 1.12 a αd spectra of solar-cell light absorbers and b EQE spectra of corresponding solar cells. In a, the αd spectra were calculated using the α spectra of Fig. 1.6 and the indicated absorber thicknesses. The EQE spectra are taken from those reported for a-SiO:H/c-Si heterojunction [23] (Fig. 2.26), CIGSe [24] (Fig. 2.9), CdTe [25] (Fig. 2.21), a-Si:H (Fig. 2.23) and CH3NH3PbI3 [26] (Fig. 16.17c (Vol. 1)) solar cells. The absorber thicknesses shown in a are consistent with those of the solar cells in b. The closed circles in a represent the EQE sensitivity limits obtained from the EQE linear fitting analyses denoted by the dotted lines in b. The positions of the EQE limits indicated by the arrows in b are identical to those of the closed circles in a

λ positions are also shown by the closed circles in Fig. 1.12a. This simple analysis reveals that the longer-λ limits observed in the EQE spectra lie at αd ∼0.01 and are much lower than αd = 1 (i.e., αdp = 1). The CIGSe solar cell shows a slightly higher EQE limit, but this is caused by the double grading structure of the Ga composition in the solar cell (see Fig. 2.8). Even though the effect of the back-side reflection is neglected completely in the above analysis, it is obvious that the EQE response in the longer λ region is governed essentially by αd. Accordingly, the fundamental potential of a solar cell can be judged from the α spectrum and the thickness of absorber layers (Fig. 1.1b).

1 Introduction

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On the other hand, the maximum values of the EQE spectra are determined by the reflection loss as well as the absorption loss induced by the free carrier absorption in a front TCO layer (Chap. 2). The incorporation of anti-reflection layers is important to suppress the reflection loss. In fact, the anti-reflection layers have been provided to the CIGSe, CdTe, a-SiO:H/c-Si solar cells that show high EQE values of ∼95% (see Fig. 1.12b). As confirmed from Fig. 1.12b, the a-Si:H solar cell exhibits lower EQE response in the longer λ region, compared with the CH3NH3PbI3 solar cell, even though Eg of a-Si:H (∼1.65 eV) is almost the same with that of CH3NH3PbI3 (1.61 eV). This is caused by the low αd values of the a-Si:H particularly in the longer λ region. Indeed, αd of the a-Si:H at 750 nm is almost 50 times smaller than that of CH3NH3PbI3. Consequently, if α (or αd) near Eg is low, the carrier generation in the longer λ region becomes difficult and Jsc decreases. The light absorption and the carrier generation can be determined more accurately from EQE simulations (Chap. 2). Figure 1.13 shows the partial EQE calculated for the state-of-the-art CIGSe solar cell with a structure of MgF2/ZnO:Al/ ZnO/CdS(n)/CIGSe(p)/MoSe2/Mo/glass [24]. In this figure, partial EQE contributions obtained at different depths from the CdS/CIGSe interface (i.e., d) and

Fig. 1.13 Normalized partial EQE calculated for different depths from the CdS/CIGSe interface and wavelengths. The dotted line represents Eg of the CIGSe at each depth. The partial EQE is consistent with the EQE spectrum of the CIGSe solar cell shown in Fig. 1.12b. The integrated Jsc values versus d and λ, calculated from the partial EQE, are also indicated. The data are adopted from [24]

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wavelengths are shown. If the partial EQE spectra obtained at different depths are integrated, the EQE spectrum shown in Fig. 1.12b is obtained. In the simulation, explicit EQE calculation has been made by incorporating the effects of the double-grading Ga profile within the CIGSe layer and the light scattering caused by the submicron textured structure (Sect. 2.2.3). In particular, the optical response of the V-shaped Ga profile, formed by conventional three-stage coevaporation, was fully simulated using a complete CIGSe optical database (Sect. 10.4 (Vol. 1)). The white dotted line in Fig. 1.13 shows the Eg positions at each depth. The EQE analysis shows that the carrier collection efficiency in the CIGSe solar cell is almost 100% and the recombination at the interfaces and grain boundaries is very small. In Fig. 1.13, the partial EQE is quite high at λ < 700 nm and decreases rapidly versus d due to high α values in this region. In contrast, the partial EQE shows lower values at λ > 700 nm and the carrier generation occurs more uniformly in the depth direction. The oscillation pattern observed in the region of d > 400 nm represents the optical interference effect. In Fig. 1.13, integrated Jsc values versus d and λ are also indicated. Rather surprisingly, the light absorption in the 1-μm-thick CIGSe bottom layer is negligible and its contribution to Jsc is quite small. From this result, it has been concluded that the CIGSe bottom layer is playing a dominant role as a back surface field with conduction band grading [24]. As confirmed from the above result, device operation can be studied more precisely from EQE characterization.

1.3.3

Optical and Recombination Losses in Solar Cells

All the current losses induced by reflection, parasitic absorption, and recombination can be assessed quantitatively based on a global EQE analysis method, in which the effects of (i) light scattering induced by textured structures and (ii) carrier recombination in light absorbers are fully accounted for. By applying this technique, the optical and recombination losses in various solar cells, including c-Si, a-Si:H, CIGSe, CZTSe, CZTS, CZTSSe, CdTe and hybrid perovskite solar cells, can be determined (Chap. 16 (Vol. 1) and Chap. 2 (Vol. 2)). It has been confirmed that the developed EQE analysis method provides excellent fitting to numerous EQE spectra reported in literature [12]. Figure 1.14 shows the example of EQE analysis performed for a record-efficiency CZTSSe solar cell reported in [8]. This solar cell was fabricated by a solution-based processing and has a conversion efficiency of 12.6% (Jsc = 35.2 mA/cm2, Voc = 0.513 V, FF = 69.8%). The structure of this solar cell is MgF2 (110 nm)/ITO (50 nm)/ZnO (10 nm)/CdS (25 nm)/CZTSSe (2.0 μm)/Mo(S)Se2 (185 nm)/Mo/glass substrate. The optical constants of these layers can be found in Part II of this book and the detailed analysis procedure is described in Sect. 2.3. In Fig. 1.14a, the EQE and absorptance spectra of the solar-cell component layers are shown, together with the reflectance spectrum indicated as 1 − R. The open circles show the experimental EQE and reflectance spectra reported in [8],

1 Introduction

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Fig. 1.14 a EQE analysis performed for a record-efficiency CZTSSe solar cell [8] using the global EQE analysis method and b optical gain and loss obtained from the analysis [12]. The EQE analysis was carried out using the optical model of MgF2 (110 nm)/ITO (50 nm)/ZnO (10 nm)/ CdS (25 nm)/CZTSSe (2.0 μm)/Mo(S)Se2 (185 nm)/Mo/glass substrate. In a, the open circles show the experimental spectra reported in [8] and the red line represents the EQE spectrum calculated assuming the carrier collection length of LC = 0.75 μm from the CdS/CZTSSe interface. The spectrum indicated by the yellow-colored region corresponds to the absorptance spectrum of the CZTSSe layer. In b, the numerical values show the corresponding current densities in units of mA/cm2

whereas the black lines indicate the calculated absorptance spectra of the component layers. In the EQE analysis, the carrier extraction from the absorber layer was modeled by considering a carrier collection length (LC) from the CdS/CZTSSe interface. The red line in Fig. 1.14a represents the calculated EQE spectrum obtained using LC as an analytical parameter. The calculation result provides excellent fitting to the experimental EQE spectrum when LC = 0.75 μm. This LC value is much smaller than the CZTSSe thickness (2.0 μm), indicating that the carrier collection occurs only in a limited depth from the CdS/CZTSSe interface. In fact, the yellow-colored region in Fig. 1.14a shows the calculated absorptance of the CZTSSe layer, but the experimental EQE spectrum shows lower values particularly in the long λ region, indicating that the significant carrier loss occurs in the CZTSSe bottom region [12]. From the difference between the EQE spectrum (red line) and the absorptance spectrum of the CZTSSe (yellow-colored region), the Jsc loss induced by the carrier recombination can be estimated directly. In Fig. 1.14b, the reflection, absorption and recombination losses deduced from the EQE analysis are summarized. For the CZTSSe layer, the maximum Jsc value attainable under the AM1.5G condition is 52.1 mA/cm2 (see also Fig. 1.4), from which the optical gain of the CZTSSe solar cell is estimated to be 67.9% (35.4 mA/cm2). In this solar cell, the reflection loss (4.5 mA/cm2), total absorption loss (7.0 mA/cm2) and recombination loss (5.2 mA/cm2) are quite large, and the moderate efficiency of ∼13% can be interpreted primarily by these losses. As confirmed from Fig. 1.14b,

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major parasitic absorption occurs in the Mo layer. This originates from very low reflectance at the CZTSSe/Mo interface (see also Fig. 12.4). In this solar cell, therefore, the long-λ EQE response is limited by the carrier recombination and the parasitic light absorption in the Mo layer. The above result demonstrates that the performance-limiting factors in solar cells can be determined quantitatively using the developed EQE analysis method. Such EQE analysis can be performed quite easily using a free EQE analysis software described in Sect. 2.7. Based on the EQE analysis result, the solar-cell processing and device structures can further be optimized quite effectively.

1.4

Overview of This Book

This volume of the book aims to provide broad understanding for the application of spectroscopic ellipsometry (SE) technique and is consisting of two major parts. In Part I, EQE analyses and advanced SE methods, which employ new optical modeling and calculation techniques, are introduced. In Part II, a quite complete optical database for numerous solar cell materials, which can be used for EQE simulations and SE analyses, is described. More specifically, after a general introduction into the topics covered by the book (Chap. 1), Part I covers the analysis of optical and recombination losses in solar cells (Chap. 2) and the optical simulations of the EQE spectra (Chap. 3). As confirmed from Fig. 1.14, the EQE analysis is a crucial technique in revealing current loss mechanisms in solar cells. In addition to conventional material and structural characterizations, SE can be employed to assess the optical properties and structures of large-area photovoltaic modules. From this point of view, the state-of-the-art SE data analysis approaches developed for textured solar cells (Chap. 4) and on-line monitoring of photovoltaic production (Chap. 5) are introduced. Explicit SE data analyses further allow real-time control of CIGSe layers fabricated using complex coevaporation processes (Chap. 6) and mapping characterization of Si thin film devices (Chap. 7). Part II summarizes (n, k) data for numerous solar-cell component layers (total 148 materials) incorporated into various solar cells. The dielectric functions of all the materials have been parameterized completely using only three dielectric function models mentioned above and their model parameters are also described. For inorganic semiconductors (Chap. 8), the complete optical data of group IV, III–V, II–VI, I–III–VI2, I2–II–IV–VI4 semiconductors are shown. The following chapter (Chap. 9) summarizes the optical data of 20 organic semiconductors. For hybrid perovskite materials (Chap. 10), the optical constants of major absorbers and their secondary phases are described. Since TCO (Chap. 11) and metal (Chap. 12) electrodes are vital components in solar cells, the optical data of various TCO and metal layers are also summarized. In particular, for important TCO materials, the variation of optical constants with carrier concentration is indicated to show the effect of the free carrier absorption. In the final chapter (Chap. 13), the optical data of substrate

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materials (glass, plastic and metal substrates) and anti-reflection coating materials are summarized. Through the above overall descriptions, in-depth knowledge and understanding for the SE technique of solar cells can be gained. Acknowledgements The author acknowledges Shohei Fujimoto for the preparation of Figs. 1.4, 1.5, 1.6 and 1.8. The author would like to thank Akihiro Nakane for the preparation of Figs. 1.3, 1.4 and 1.5.

References 1. S. Minoura, K. Kodera, T. Maekawa, K. Miyazaki, S. Niki, H. Fujiwara, J. Appl. Phys. 113, 063505 (2013) 2. M.A. Green, K. Emery, Y. Hishikawa, W. Warta, E.D. Dunlop, D.H. Levi, A.W.Y. Ho-Baillie, Prog. Photovolt. 25, 3 (2017) 3. The numerical data can be downloaded at http://pveducation.org/pvcdrom/appendices/ standard-solar-spectra 4. M.A. Green, K. Emery, Y. Hishikawa, W. Warta, E.D. Dunlop, Prog. Photovolt. 21, 1 (2013) 5. P. Jackson, D. Hariskos, R. Wuerz, O. Kiowski, A. Bauer, T.M. Friedlmeier, M. Powalla, Phys. Status Solidi RRL 9, 28 (2015) 6. Y.S. Lee, T. Gershon, O. Gunawan, T.K. Todorov, T. Gokmen, Y. Virgus, S. Guha, Adv. Energy Mater. 5, 1401372 (2015) 7. B. Shin, O. Gunawan, Y. Zhu, N.A. Bojarczuk, S.J. Chey, S. Guha, Prog. Photovolt. 21, 72 (2013) 8. W. Wang, M.T. Winkler, O. Gunawan, T. Gokmen, T.K. Todorov, Y. Zhu, D.B. Mitzi, Adv. Energy Mater. 4, 1301465 (2014) 9. S. Kim, K.M. Kim, H. Tampo, H. Shibata, S. Niki, Appl. Phys. Express 9, 102301 (2016) 10. H.D. Kim, H. Ohkita, H. Benten, S. Ito, Adv. Mater. 28, 917 (2016) 11. W.S. Yang, J.H. Noh, N.J. Jeon, Y.C. Kim, S. Ryu, J. Seo, S.I. Seok, Science 348, 1234 (2015) 12. A. Nakane, H. Tampo, M. Tamakoshi, S. Fujimoto, K.M. Kim, S. Kim, H. Shibata, S. Niki, H. Fujiwara, J. Appl. Phys. 120, 064505 (2016) 13. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, West Sussex, UK, 2007) 14. S. Adachi, J. Appl. Phys. 53, 8775 (1982) 15. H. Sai, K. Saito, N. Hozuki, M. Kondo, Appl. Phys. Lett. 102, 053509 (2013) 16. A. Luque, S. Hegedus, Handbook of Photovoltaic Science and Engineering (Wiley, West Sussex, UK, 2011) 17. W.B. Jackson, S.M. Kelso, C.C. Tsai, J.W. Allen, S.-J. Oh, Phys. Rev. B 31, 5187 (1985) 18. W.-J. Yin, T. Shi, Y. Yan, Adv. Mater. 26, 4653 (2014) 19. T.M. Brenner, D.A. Egger, L. Kronik, G. Hodes, D. Cahen, Nat. Rev. Mater. 1, 15007 (2016) 20. R.A. Street, Hydrogenated Amorphous Silicon (Cambridge Univ. Press, Cambride, 1991) 21. S. De Wolf, J. Holovsky, S.-J. Moon, P. Löper, B. Niesen, M. Ledinsky, F.-J. Haug, J.-H. Yum, C. Ballif, J. Phys. Chem. Lett. 5, 1035 (2014) 22. G.E. Jellison Jr., F.A. Modine, Appl. Phys. Lett. 69, 371 (1996). Erratum. Appl. Phys. Lett. 69, 2137 (1996). 23. H. Fujiwara, H. Sai, M. Kondo, Jpn. J. Appl. Phys. 48, 064506 (2009) 24. T. Hara, T. Maekawa, S. Minoura, Y. Sago, S. Niki, H. Fujiwara, Phys. Rev. Appl. 2, 034012 (2014)

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25. T. Aramoto, S. Kumazawa, H. Higuchi, T. Arita, S. Shibutani, T. Nishio, J. Nakajima, M. Tsuji, A. Hanafusa, T. Hibino, K. Omura, H. Ohyama, M. Murozono, Jpn. J. Appl. Phys. 36, 6304 (1997) 26. J.H. Heo, D.H. Song, H.J. Han, S.Y. Kim, J.H. Kim, D. Kim, H.W. Shin, T.K. Ahn, C. Wolf, T.-W. Lee, S.H. Im, Adv. Mater. 27, 3424 (2015)

Part I

Application of Ellipsometry Technique

Chapter 2

Analysis of Optical and Recombination Losses in Solar Cells Hiroyuki Fujiwara, Akihiro Nakane, Daisuke Murata, Hitoshi Tampo, Takuya Matsui and Hajime Shibata

Abstract For efficient optimization of solar-cell device structures and processing, it is essential to reveal the performance-limiting optical and physical factors in solar cells. Quite fortunately, a global solar-cell characterization method has recently been developed from which the parasitic light absorption and carrier recombination in the devices are evaluated systematically based on external quantum efficiency (EQE) analysis. In this new method, the optical and recombination losses in complex solar cell structures are readily determined within the framework of a rather simple optical admittance method. The EQE analysis method described in this chapter is appropriate for a wide variety of photovoltaic devices, including crystalline Si (c-Si), hydrogenated amorphous silicon (a-Si:H), Cu(In,Ga)Se2 chalcopyrite, Cu2ZnSn(S,Se)4 kesterite, CdTe zincblende and hybrid perovskite solar cells, and provides excellent fitting to numerous EQE spectra obtained experimentally. This chapter introduces the basic concept of the global EQE analysis method in which the effects of (i) light scattering by submicron textures and (ii) carrier recombination in light absorbers are fully incorporated. As examples, the EQE analyses of Cu(In,Ga)Se2, Cu2ZnSnSe4, Cu2ZnSnS4, CdTe, a-Si:H and c-Si solar cells are described. Based on the analysis results, we will further discuss the carrier loss mechanisms in different types of photovoltaic devices.

2.1

Introduction

The performance of solar cells is affected by a variety of optical and physical characteristics of solar-cell component layers and, in developing photovoltaic devices with high efficiencies, identification and the following improvement of the H. Fujiwara (✉) ⋅ A. Nakane ⋅ D. Murata Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] H. Tampo ⋅ T. Matsui ⋅ H. Shibata Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Japan © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_2

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limiting factors are crucial. From this point of view, the development process of solar cells can be compared to water in a barrel [1]. Figure 2.1 explains the improvement of a solar cell efficiency using this analogy. In this illustration, water is pouring into a barrel consisting of staves with different lengths, and the pouring water is an analogy of sunlight. The staves of the barrel represent the characteristics of each solar cell component and the stave length becomes shorter if the specific component shows poor characteristics. In Fig. 2.1, the examples of the important solar-cell components, including a transparent conductive oxide (TCO) layer and series resistance (Rs), are indicated. In Fig. 2.1, the water level in the barrel corresponds to the conversion efficiency of the solar cell, and the solar-cell efficiency is governed by the most limiting factor (Law of the minimum). In other words, the solar cell performance is determined by the shortest stave and the conversion efficiency may not improve unless the characteristics of the shortest stave are improved. Even when we improve such a limiting factor, the solar cell efficiency may not show a notable increase if there is still another component that has poor properties. Unfortunately, the finding of the limiting factors of solar cells is generally quite difficult, and many researches rely on a trial and error approach to improve solar cell efficiencies. As a result, the research efforts are often ineffective, and the continuous research is necessary over a quite long period of time (often a few decades). One quite effective method that can be applied for the accurate evaluation of performance-limiting optical and physical factors in solar cells is external quantum efficiency (EQE) analysis [2–18]. In fact, the EQE analysis is the only method that allows the quantitative assessment of unfavorable optical absorption (i.e., parasitic

Fig. 2.1 Schematic illustration explaining the development of a high-efficiency solar cell. The pouring water is an analogy of sunlight, while the lengths of the staves indicate the characteristics of each solar cell component. The conversion efficiency is represented by the water level

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absorption) in solar cells. Since the EQE spectra contain the depth information due to the wavelength (λ)-dependent penetration depth of light, the carrier recombination near the front and rear interfaces can further be determined from the EQE response in the short and long λ regions, respectively (Sect. 2.3.3). Figure 2.2 explains how the EQE spectrum changes with the parasitic light absorption and carrier recombination in solar cells. The EQE represents the percentage of photons that actually contribute to generate the current in solar cells. In Fig. 2.2a, we assume a hypothetical situation that all the sunlight is absorbed completely in a semiconducting absorber with zero reflectance (i.e., R = 0). In this case, the EQE values become 100% below λ which corresponds to the band gap (Eg) of the semiconductor [λEg(SC)]. In the example of Fig. 2.2, λEg(SC) is assumed to locate in the infrared region. In a metal/semiconductor structure (Fig. 2.2b), the light reflection (R >0) reduces the EQE response in a wide region from the ultraviolet (UV) to the visible region. The reflectance components of this structure can be categorized into the front surface (Rfront) and rear surface (Rrear) contributions. The constant contribution of R in the UV/visible region is consistent with Rfront, whereas R increases near λEg(SC), as the light absorption within the absorber becomes weaker and Rrear increases. Thus, R in the transparent region is expressed by Rfront + Rrear. In Fig. 2.2b, the onset of the light absorption in the semiconductor agrees with the position of λEg(SC). Nevertheless, if the tail-state absorption is present, we observe non-zero EQE values even at λ > λEg(SC). It can be seen from Fig. 2.2b that the light absorption in the metal electrode layer becomes significant near λEg(SC) due to higher light transmission in this region. However, the light absorption in the metal layer is governed by the optical constants of the semiconductor and metal and, when the reflectance at the semiconductor/ metal interface is low, more light is absorbed by the metal. The reflectances of various rear metal electrodes in crystalline Si (c-Si), Cu(In,Ga)Se2 (CIGSe) and hybrid perovskite [HC(NH2)2PbI3] solar cells are summarized in Fig. 12.3. When a front TCO electrode, such as In2O3:Sn (ITO) and ZnO:Al, is formed (Fig. 2.2c), the parasitic light absorption in the TCO reduces the EQE. In particular, there exist two absorption processes in TCO materials: i.e., interband transition and free carrier absorption (see Fig. 18.6 in Vol. 1). The strong reduction of the EQE in the UV region is caused by the TCO interband transition that occurs below λ corresponding to Eg of the TCO [i.e., λ ≤ λEg(TCO)]. On the other hand, the TCO absorption above λEg(TCO) is attributed to the free carrier absorption (Fig. 18.8 in Vol. 1). Due to the light absorption in the TCO layer, the internal quantum efficiency (IQE) defined by the following equation also decreases. IQE = EQE ̸ð1 − RÞ.

ð2:1Þ

The IQE shows how efficiently the absorbed photons (not incident photons) are converted into the photocurrent and the IQE spectrum is obtained by normalizing the EQE spectrum using the absorption component (i.e., 1 − R). In c-Si solar cells

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◀Fig. 2.2 Variation of EQE spectrum with solar cell structure: EQE spectra of a a hypothetical

perfect absorber with zero reflectance (R = 0), b an absorber/metal structure, c a transparent conductive oxide (TCO)/absorber/metal structure, d a TCO/doped layer/absorber/metal structure, and e a TCO/doped layer/absorber/metal structure with a recombination layer within the absorber layer. The position of λEg shows λ that corresponds to Eg of semiconductor (SC), TCO and doped layers. In the figure, λEg(SC) is assumed to be in the infrared region. In b, Rfront represents the reflectance contribution induced by the front surface reflection, while Rrear shows that caused by the rear-side reflection

that incorporate no TCO layers, IQE of ∼100% is observed [19, 20], whereas the maximum IQE is generally limited to 80–95% for solar cells with TCO layers [5–7, 10–12, 17, 18]. In Fig. 2.2d, a doped layer is inserted at the TCO/semiconductor interface. In general, the doped layers in solar cells exhibit the intense light absorption and deteriorate the EQE response particularly in the short λ region (see Sect. 2.2.3). Since the parasitic light absorption in the TCO and doped layers occurs sequentially from the upper layer, the presence of the doped layer leads to the additional EQE reduction below λEg of the doped layer [i.e., λ ≤ λEg(doped)]. In photovoltaic devices, the extraction of photo-generated carriers from the semiconductor light absorber is an essential process and the presence of recombination centers within absorber layers reduces the short-circuit current density (Jsc) significantly. The effect of the recombination generally becomes more severe in a solar-cell bottom region, where the generated carriers need to reach the front interface through carrier diffusion [18]. As shown in Fig. 2.2e, if the carrier recombination occurs at the semiconductor/metal rear interface, the EQE response in the longer λ region decreases. When the photogenerated carriers recombine in a solar-cell front region, the EQE values in the short λ region decrease, which is similar to the case of the doped layer in Fig. 2.2d. In other words, the carrier recombination in the front and rear interface regions can be characterized quantitatively based on detailed EQE analyses (Sect. 2.3.3). Often, Eg of the absorber layer is extracted from the EQE analysis of the longer λ region [21–25]. In this case, however, Eg will be overestimated seriously if the carrier recombination in a solar-cell bottom region is significant [18], as confirmed from Fig. 2.2e. Unfortunately, the EQE analyses of conventional solar cells have been rather difficult due to the presence of textured structures. Figure 2.3 shows the scanning electron microscope (SEM) images of (a) CIGSe and (b) Cu2ZnSnSe4 (CZTSe) solar cells, obtained from the same samples reported in [16] and [18], respectively. The CIGSe solar cell in Fig. 2.3a, fabricated by a conventional three-stage coevaporation process [26–28], has a structure of MgF2/ZnO:Al/ZnO/CdS/CIGSe/ Mo/glass with Jsc = 34.2 mA/cm2, a open-circuit voltage of Voc = 674 mV and a fill factor of FF = 0.725 (conversion efficiency: 16.7%) [16]. The solar cell structure of CZTSe is quite similar to that of the CIGSe, although there is no MgF2 anti-reflection layer in the solar cell. The conversion efficiency of this solar cell is 8.5% with Jsc = 33.4 mA/cm2, Voc = 418 mV, and FF = 0.606 [18]. It can be seen from Fig. 2.3 that these solar cells have submicron-size natural textures ( 0.4 μm, shows the interference effect induced by the thin film structure. The dotted line represents Eg of the CIGSe at each depth determined from xEQE(d). In particular, at dv = 0.54 μm, Eg shows the lowest value of 1.12 eV (xv = 0.18) and the upper limit for the light absorption extends into the longer λ region. In Fig. 2.12c, the partial absorptance of the CIGSe layer is integrated toward the depth to deduce the contribution of the absorptance at each depth for Jsc. The light absorption in the CIGSe layer occurs predominantly at d < 600 nm and Jsc increases rapidly in this thickness region. In contrast, the increase in Jsc is almost negligible in the CIGSe bottom region. If the CIGSe layer is divided into the two sublayers with an equal thickness of 900 nm, Jsc generated in the top sublayer accounts for 95% of the total Jsc. Based on this result, it has been concluded that the 1-μm-thick CIGSe bottom layer with the Ga-grading profile plays a dominant role as the back-surface field (BSF) layer in CIGSe solar cells [16].

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As confirmed from the above analysis example, the ARC and ERS methods are quite simple but provide excellent fitting to the experimental EQE spectrum. From this method, the carrier generation within the absorber layer and the Jsc losses due to parasitic light absorption can be assessed quantitatively. Since the calculation cost of the ARC and ERS methods is quite low, these EQE analyses can be made using conventional computers on a routine basis.

2.3

e-ARC Method

In the above EQE analyses, the influence of the carrier recombination has been neglected. However, the photocurrent reduction by carrier recombination can be modeled quite simply by considering a carrier collection length in the absorber layer. By incorporating the effect of the carrier recombination within the framework of the ARC method, a global EQE analysis scheme has been developed [18]. From this extended ARC method (e-ARC method), optical and recombination losses in various thin-film solar cells can be estimated rather easily. In this section, the basic concept of the e-ARC method is explained.

2.3.1

Recombination Model

In solar cells, different types of recombinations occur within the semiconductor bulk layer and at the front/rear interfaces (see also Fig. 1.2). Figure 2.13 shows the carrier recombination processes in a p-n junction solar cell. In this figure, only the movement of the photogenerated electrons is shown. In this solar cell, the photocarriers created within a distance of LC from the n/p junction interface are collected, while the carriers generated in the solar cell bottom region are lost due to the recombination at defects formed in the bulk layer or at the p layer/metal interface. In this recombination model, LC defines the carrier collection length and all the carriers generated within LC from the front interface are assumed to contribute to the current generation (i.e., EQE). This can be described quite simply by HðλÞ = 1 − exp½ − αðλÞLC ,

ð2:33Þ

where H and α show the carrier collection efficiency and the absorption coefficient of the absorber (semiconductor) layer. This model is equivalent to the light absorption expressed by the well-known Beer’s law, A(λ) = 1 − exp[−α(λ)d], where d is a distance from the surface or interface (see Fig. 1.11). Thus, H(λ) represents the light absorption at the depth LC from the surface (or interface) of materials having infinite thickness. In the model of (2.33), therefore, the optical confinement effect, induced by the back-side reflection and the resulting multiple light reflections

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Fig. 2.13 Carrier recombination processes in a p-n junction solar cell. In this figure, only the photogenerated electrons are shown. The LC represents the carrier collection length defined by (2.33) and, in the model, the carriers generated deeper than LC are assumed to recombine. The LC is further expressed as LC = W + LD (2.34), where W and LD are the depletion layer thickness and carrier diffusion length, respectively

within the absorber layer, has been neglected. By applying (2.33) directly to IQE spectra, simple optical simulations have also been performed [40, 41]. In the above model, the influences of the carrier diffusion and carrier drift in the space-charge region are not described separately. Moreover, the effects of the band offset and the carrier recombinations that occur in the bulk, interface and grain-boundary regions are not specifically modeled. The significance of the H(λ) model is that all the complex effects concerning the carrier collection are represented by a single analysis parameter of LC. As shown in Fig. 2.13, the relationship of LC with a diffusion length (LD) can be described by LC = W + LD ,

ð2:34Þ

where W indicates the depletion layer thickness [40]. For H(λ), a more exact equation has been derived by solving the carrier continuity equation [2, 3]: HðλÞ = 1 − exp½ − αðλÞW ̸½1 + αðλÞLD .

ð2:35Þ

In this model, the carrier collection is described by the two parameters (W, LD). When the above model is applied to EQE fitting analysis, however, W and LD show a strong correlation and it is rather difficult to obtain the unique solution [18]. In reported studies [21, 42], therefore, W has been determined from separate experiments using a capacitance-voltage technique. Figure 2.14 explains the calculation procedure of the e-ARC method. In this calculation example, the EQE spectrum of a CZTSe solar cell is simulated assuming an optical model of ZnO:Al (350 nm)/ZnO (50 nm)/CdS (50 nm)/CZTSe (1500 nm)/Mo. The optical constants of the CZTSe were calculated assuming Eg = 1.07 eV based on a procedure described in Sect. 2.3.2. In the first step of the e-ARC simulation, the absorptance spectrum of the light absorber is calculated

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Fig. 2.14 Calculation procedure of the e-ARC method: a Reflectance spectra calculated assuming a flat structure (Rflat) and an anti-reflection condition (RARC), together with the absorptance spectra of the CZTSe layer, Aflat and AARC, obtained from Rflat and RARC, respectively, b carrier collection efficiency H(λ) calculated from α(λ) of the CZTSe using different values of the carrier collection length (LC), and c EQE spectra of the CZTSe solar cell calculated from the results of a and b. The EQE simulations were performed using an optical model of ZnO:Al (350 nm)/ZnO (50 nm)/CdS (50 nm)/CZTSe (1500 nm)/Mo. In a, the red circles correspond to the Rmin positions indicated in Fig. 2.10

using the ARC method. In Fig. 2.14a, the obtained spectrum is shown as AARC, together with RARC as well as Rflat and Aflat determined from the optical admittance method. The calculation procedures of RARC and AARC are exactly the same as those shown in Fig. 2.10. It can be seen that the interference fringe is relatively large in the CZTSe solar cell and AARC is quite different from Aflat. In other words, the texture effect is rather significant in the CZTSe solar cell and the yellow-colored region indicated in Fig. 2.14a is absorbed additionally by applying the anti-reflection condition. In the second step, H(λ) is calculated from (2.33) by selecting LC. In Fig. 2.14b, several H(λ) values calculated from α(λ) of the CZTSe using different LC values are shown. When LC is infinite (LC = ∞), we obtain H(λ) = 1 in the energy region above the absorption edge of the CZTSe (λ ≤ 1441 nm in Fig. 2.14b). As LC decreases, H in the longer λ region gradually decreases. In the calculation of H(λ)

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using (2.33), however, it is necessary to use unrealistic LC values that are far larger than the total thickness of the absorber layer (1.5 μm in Fig. 2.14). Thus, LC defined by (2.33) should be considered as a parameter (reference) value. Nevertheless, when LC is smaller than the absorber layer thickness, LC approximates a real physical value. In the e-ARC method, from AARC(λ) and H(λ), the EQE spectrum is calculated simply by EQEðλÞ = AARC ðλÞHðλÞ.

ð2:36Þ

In Fig. 2.14c, the EQE spectra calculated from the e-ARC method using AARC in Fig. 2.14a and H(λ) in Fig. 2.14b are shown. In the case of LC = ∞ [i.e., H(λ) = 1], we obtain EQE(λ) = AARC(λ) (i.e., the ARC method in Fig. 2.10). When the EQE spectrum is calculated from the e-ARC method, the EQE response in the longer λ region decreases as LC decreases due to the limited carrier extraction and LC is deduced from the fitting analysis of the EQE spectrum. Based on the EQE calculation result, the Jsc loss due to the carrier recombination is estimated by Jloss =

qλ hc

Z ½AARC ðλÞ − EQEðλÞFðλÞdλ.

ð2:37Þ

In the e-ARC method, therefore, the recombination loss is calculated quantitatively using LC as a sole parameter. It should be noted that, when the absorber layer thickness itself is modified, the optical interference and back-side reflection in solar cells change significantly [17]. Thus, it is necessary to model the carrier generation and collection separately. The above analysis scheme can also be applied for the ERS method. In this case, we employ EQE(λ) = AERS(λ)H(λ), which will be referred to as the e-ERS method. In the e-ARC and e-ERS methods, the carrier recombination in the solar cell bottom region is assumed. In some solar cells, however, the carriers recombine predominantly near the front interface (i.e., n/p interface in Fig. 2.13). In this case, the carrier recombination can be modeled by simply dividing an absorber layer into two sublayers and treating a top sublayer near the front interface as a “dead layer” that allows no carrier extraction, as applied for the EQE analyses of hybrid perovskite solar cells (see Fig. 16.17 in Vol. 1).

2.3.2

Analysis of a CZTSe Solar Cell

The submicron-textured CZTSe solar cell shown in Fig. 2.3b has been analyzed by applying the e-ARC method [18]. Figure 2.15 shows (a) the EQE analysis result of the CZTSe solar cell and (b) the optical gain and loss obtained from the analysis [18]. The EQE analysis was carried out using an optical model consisting of ZnO: Al (350 nm)/ZnO (50 nm)/CdS (70 nm)/CZTSe (1260 nm)/MoSe2 (150 nm)/Mo.

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Fig. 2.15 a EQE analysis of the CZTSe solar cell performed by using the e-ARC method and b optical gain and loss obtained from the analysis [18]. The EQE analysis was carried out for the CZTSe solar cell shown in Fig. 2.3b using the optical model of ZnO:Al (350 nm)/ZnO(50 nm)/ CdS (70 nm)/CZTSe (1260 nm)/MoSe2 (150 nm)/Mo. In a, the open circles show the experimental spectrum and the red line represents the EQE spectrum calculated from the e-ARC method assuming LC = 0.57 μm. The spectrum indicated by the yellow-colored region corresponds to the absorptance spectrum (LC = ∞) of the CZTSe layer. In b, the numerical values show the corresponding current densities in units of mA/cm2

The thicknesses of these layers were determined from the TEM observation. The optical effect of the void-rich CZTSe structure observed in Fig. 2.3b was also taken into account by using two sublayers for the CZTSe. In particular, for the CZTSe bottom sublayer with a thickness of 310 nm, a void volume fraction of 30 vol.% was assumed. The optical properties of this bottom sublayer were calculated by the Bruggeman effective-medium approximation [36]. For the CZTSe layer, the reported optical constants (Fig. 8.30) were used, and the change of Eg with the Cu/(Zn + Sn) ratio was further considered. This Eg shift in the CZTSe was modeled by sliding the whole spectrum toward higher energy. In this case, the ε2 amplitude was reduced slightly so that the sum rule described by (16.1) in Vol. 1 was satisfied [18]. As a result, the EQE fitting analysis of Fig. 2.15a was implemented using two analytical parameters: i.e., LC and Eg of the CZTSe. In Fig. 2.15a, the open circles show the experimental EQE spectrum, whereas the black lines represent the RARC and absorptance spectra. The EQE spectrum obtained from the e-ARC fitting analysis is indicated by the red line. As confirmed from this figure, the calculated spectrum shows excellent agreement when LC = 0.57 μm and Eg = 1.07 eV. It can be seen that, compared with AARC of the CZTSe layer (LC = ∞), the experimental EQE spectrum shows quite low values particularly in the long λ region. This result indicates the significant carrier loss within the CZTSe layer. In particular, the estimated LC value of ∼0.6 μm is much smaller than the total thickness of the CZTSe absorber layer (∼1.3 μm), confirming quite poor carrier collection in the solar cell bottom region.

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The optical losses of the CZTSe solar cell shown in Fig. 2.15b are rather similar to those of the CIGSe solar cell in Fig. 2.11b. However, the CZTSe solar cell shows a large recombination loss of 6.5 mA/cm2 and the resulting optical gain becomes smaller (60.5%). The result of Fig. 2.15 indicates that, based on the EQE analysis using the e-ARC method, all the reflection, absorption and recombination losses can be determined quantitatively even when solar cells have quite complex submicron textures represented by Fig. 2.3b. Figure 2.16 summarizes the results of the EQE fitting analyses performed for the CZTSe solar cell using different optical models. The experimental data (gray open circles) correspond to those shown in Fig. 2.15a and the result of Model1 indicates that obtained from the e-ARC analysis (LC = 0.57 μm). In Model2, the CZTSe layer is divided into active and dead layers, and the EQE fitting was implemented by adjusting the active layer thickness (dA). In Model3, the thickness of the CZTSe layer in the optical model was changed. As shown in Fig. 2.16, all the models provide similar fittings but Model1 provides the best matching particularly in the longer λ region (1100 < λ < 1300 nm). On the other hand, dA obtained from Model2 (0.56 μm) is almost the same as LC = 0.57 μm. In other words, LC obtained from the EQE fitting analysis is basically equivalent to the thickness of the absorber layer where the carrier extraction occurs predominantly. When the total absorber thickness is changed in the optical model (Model3), the influence of the back-side reflection becomes stronger and the effective thickness obtained from the analysis (d = 0.45 μm) becomes smaller, compared with LC and dA.

Fig. 2.16 Results of EQE fitting analyses performed for the CZTSe solar cell using different optical models: i.e., Model1: e-ARC method, Model2: two sublayer model with the bottom layer being the optical dead layer, Model3: optical model with a thinner CZTSe layer. The experimental spectrum (gray open circles) and the result of Model1 are identical to those of Fig. 2.15a

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Interpretation of EQE Spectra

To understand the effects of the carrier recombinations at the front and rear interfaces of a light absorber, the partial absorptance of the above CZTSe solar cell was calculated by dividing the CZTSe layer into 1-nm-thick sublayers. Figure 2.17a shows the α spectrum of the CZTSe layer and the corresponding penetration depth of light calculated by dp = 1/α (see Fig. 1.11). As confirmed from this figure, dp is small ( 900 nm due to the lower α values. To visualize the influence of the carrier recombination, we assume a front (rear) dead layer with a thickness of df (dr). The thicknesses of these dead layers used for the calculations are indicated by the dotted lines in Fig. 2.17b. By assuming no carrier extraction from these layers, the EQE spectra can be calculated. Figure 2.17c shows the EQE spectra obtained when df is increased from 0 to 80 nm. Since the light is absorbed strongly near the CdS/CZTSe interface, the slight increase in df leads to the significant reduction in the short λ response, whereas the EQE in the longer λ region shows the minor reduction as the carriers are generated uniformly in this region. In contrast, when dr is increased in a range of 0–800 nm (Fig. 2.17d), only the longer λ response decreases, since almost no carriers are generated at the corresponding depth at λ < 700 nm. It should be emphasized that, at λ ≥ 900 nm, the holes and electrons generated near the front and rear interfaces, respectively, need to travel the whole layer to generate the current in the device. Accordingly, short LC lowers the partial EQE particularly in the longer λ region. It is evident from the above results that the effect of the front carrier recombination appears as the EQE reduction in the short λ region, whereas the carrier recombination in the rear interface region reduces the EQE in the longer λ region. Accordingly, from the comparison with the A spectrum of the absorber layer (i.e., AARC), the carrier recombination region can be speculated rather easily. In the e-ARC analysis, the effect of dr is expressed by LC (see Fig. 2.16), whereas df is modeled directly using a sublayer. However, depending on devices, the validity of the recombination model needs to be confirmed. If the thickness of the absorber layer can be changed, several solar cells can be analyzed to confirm the consistency.

2.4

EQE Analysis Examples

The e-ARC and e-ERS methods have been applied successfully to the EQE analyses of numerous solar cells based on CZTSe, CZTS, CZTSSe, CdTe, and hybrid perovskite solar cells [18]. In this section, the EQE analyses of CZTSe, CZTS and CdTe solar cells are introduced briefly. This section further establishes the EQE analysis method for an a-Si:H p-i-n solar cell.

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CZTSe and CZTS Solar Cells

The EQE spectra of various CZTSe and CZTS solar cells can be analyzed using the same analysis procedure described above. Figure 2.18 shows the results of the EQE fitting analyses performed for reported solar cells of (a) CZTSe [21–25] and (b) CZTS [43–47]. The open circles show the experimental EQE spectra of the reported solar cells, fabricated by coevaporation processes [21, 24, 25, 43], a solution-based processing using hydrazine [22], a selenization process [23] and sulfurization processes [44–47], whereas the solid lines indicate the fitting results obtained using the e-ARC method. For the EQE analysis of [21], however, the ERS method was applied as RERS was reported for this solar cell. To perform the above EQE analyses, the thicknesses of the solar-cell component layers were extracted from the descriptions and the SEM images of each reference. In the analyses, the TCO optical properties and the CdS thickness were adjusted slightly. Although there is slight uncertainty for the TCO optical constants in the EQE analyses for reported spectra, the TCO optical properties can still be deduced from the EQE response in the visible region (λ ∼600 nm) and the analysis of LC can be performed. In the CZTS solar cell analyses, the reported optical constants of CZTS (Fig. 8.29) were used and the variation of Eg with the Cu/(Zn + Sn) ratio was also taken into account [18]. As a result, the EQE fitting analyses of Fig. 2.18 were carried out using LC and Eg as fitting parameters. It can be seen that all the calculated results show excellent agreement with the experimental spectra, independent of the detailed solar cell structure and processing method. Accordingly, if the layer thicknesses are known, the quantitative EQE

Fig. 2.18 Experimental EQE spectra of a CZTSe solar cells reported in [21–25] and b CZTS solar cells reported in [43–47] (open circles), together with the results of the EQE fitting analyses performed for these solar cells using the e-ARC and e-ERS methods (solid lines) [18]. The LC values obtained from the EQE analyses are also shown

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analysis can be performed rather easily from the e-ARC and e-ERS methods using the optical database summarized in Part II of this book. The EQE analyses of Fig. 2.18 result in the LC values of 0.17–2.30 μm for the CZTSe solar cells and 0.23–1.30 μm for the CZTS solar cells with the Eg values in ranges of 0.98– 1.07 eV (CZTSe) and 1.44–1.50 eV (CZTS). The EQE spectrum of [21] in Fig. 2.18a is obtained from a record-efficiency CZTSe solar cell with a conversion efficiency of 11.6% (Jsc = 40.6 mA/cm2, Voc = 423 mV, FF = 0.673). This solar cell has a very uniform thin film structure with large CZTSe grains and shows the highest LC value of 2.3 μm. In Fig. 2.18, with decreasing LC, the EQE response in the longer λ region decreases systematically in both CZTSe and CZTS solar cells, indicating that Jsc of these solar cells is limited by the carrier recombination that occurs in the solar-cell bottom region. For the CZTSe solar cells, Jsc increases largely from 27.0 mA/cm2 [25] to 40.6 mA/cm2 [21] with LC. The LC values extracted from the CZTS solar cells are smaller than those of the CZTSe solar cells. Moreover, in the EQE spectra of [45, 47] at λ = 500–600 nm, the experimental EQE values are slightly lower, compared with the calculated EQE values, suggesting that the carrier recombination occurs slightly near the CdS/CZTS front interface. Other EQE spectra reported for CZTSe [48–51], CZTS [52–55] and CZTSSe [56–64] solar cells have also been characterized by the e-ARC method. To analyze the CZTSSe solar cells, a CZTSSe optical database has been developed [18], from which the Cu2ZnSn(SxSe1-x)4 optical constants for the arbitrary S composition x can be extracted using the energy shift model (Sect. 10.4.1 in Vol. 1). The results calculated for selected compositions (x = 0.2, 0.4, 0.6 and 0.8) can be found in Fig. 8.31. In the EQE analyses of the CZTSSe solar cells, excellent fittings, similar to those in Fig. 2.18, have also been confirmed [18]. Figure 2.19 summarizes (a) Jsc, (b) Voc, (c) FF and (d) efficiency of the analyzed CZTSe [21–25, 48–51], CZTS [43–47, 52–55] and CZTSSe [56–64] solar cells as a function of LC extracted from the EQE analyses [18]. The result for Jsc (Fig. 2.19a) indicates clearly that the overall LC values of the CZTS solar cells are smaller than those of the CZTSe and CZTSSe solar cells. The solid lines indicate the simulation results obtained assuming Eg of 1.04 eV (CZTSe), 1.08 eV (CZTSSe) and 1.46 eV (CZTS). These calculations were performed using the structure of ZnO:Al (350 nm)/ZnO (50 nm)/CdS (70 nm)/Absorber (CZTSe, CZTS or CZTSSe: 2.0 μm)/MoSe2 (150 nm)/Mo. In Fig. 2.19a, Jsc increases as Eg of the absorber material decreases. The simulated Jsc reproduces the experimental result quite well, although the experimental data are scattered slightly due to the difference in the device structure and the material optical properties. For the variation of Voc with LC, CZTS shows the larger increase, compared with the CZTSe and CZTSSe. In particular, Voc of the CZTSe is rather independent of LC in the wide range. From the above results, the carrier recombination mechanism can be discussed further. Figure 2.20 shows the schematic band diagram proposed for the CZTSe solar cells [18]. In this figure, the band diagram near the MoSe2 is not shown, as the band diagram at the rear interface remains controversial [65, 66]. For CZTSe solar cells, a quite large conduction band offset at the CdS/CZTSe interface

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Fig. 2.19 a Jsc, b Voc, c FF and d efficiency of reported CZTSe [21–25, 48–51], CZTS [43–47, 52–55] and CZTSSe [56–64] solar cells as a function of LC deduced from the EQE analyses. The solid lines indicate the variations of Jsc with LC, calculated assuming Eg of 1.04 eV (CZTSe), 1.08 eV (CZTSSe) and 1.46 eV (CZTS)

(ΔEC = 0.48–0.6 eV) has been confirmed [67, 68]. As known well [42, 69], CZT (S)Se layers generally exhibit p-type conductivity and the depletion region is formed by the n-type CdS. It has been reported that the hole carrier concentration of a CZTSe layer is 3 × 1016 cm−3 and the resulting W is 0.2 μm [69]. In the CZTSe solar cells, therefore, the flat-band formation is expected to occur in the CZTSe bottom region. If we assume that W = 0.2 μm and LC = 0.6 μm (Fig. 2.15), we obtain LD = 0.4 μm from (2.34). As illustrated in Fig. 2.20, since the CZTSe layer thickness (>1 μm) is thicker than LD (or LC), many photocarriers generated in the flat band region are lost by the intense carrier recombination. There are two possible recombination passes that are expected to lower LD in CZTSe solar cells: i.e., the recombinations (i) at the CZTSe/MoSe2 interface and (ii) within the CZTSe bulk layer, as depicted in Fig. 2.20. The low Voc observed in the CZTSe solar cells is independent of LC (Fig. 2.19b) and this can be interpreted

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Fig. 2.20 Schematic band diagram proposed for the CZTSe solar cell [18]. The carrier recombination processes in the bulk and rear interface regions are also indicated. The rough scales of LC, LD and W are also shown

by the intense rear-interface recombination. In fact, when a TiN barrier layer is provided on the Mo substrate, the EQE response in the longer λ region improves significantly [70]. In the CZTSe solar cell, therefore, the insertion of a BSF structure is expected to be effective for the suppression of the carrier recombination in the bottom region. In Fig. 2.19b, on the other hand, Voc of the CZTS solar cells increases rather significantly with LC. This result implies that Voc of the CZTS solar cells is limited by the recombination within the CZTS bulk layer. The low FF values of the CZTS solar cells also support the lower quality of the CZTS absorber layers. In this way, the recombination processes in solar cells can be discussed based on the variation of solar cell characteristics with LC. It can be seen from Fig. 2.19d that the conversion efficiency of the solar cells increases systematically with LC, confirming that LC is a critical parameter of solar cells.

2.4.2

CdTe Solar Cell

By applying the e-ARC method, the EQE spectrum of a reported CdTe solar cell [71], fabricated by a standard closed-space sublimation process [72, 73], has been analyzed [18]. This CdTe solar cell has a conversion efficiency of 16.0% (Jsc = 26.1 mA/cm2, Voc = 840 mV, FF = 0.731) with a structure consisting of MgF2/glass/ITO/CdS/CdTe/carbon electrode [71]. Since this solar cell has a superstrate structure, the influence of the glass substrate needs to be calculated according to the procedure described in Sect. 2.2.2. Figure 2.21 shows (a) the EQE analysis result of the CdTe solar cell and (b) the optical gain and loss obtained from the analysis [18]. The shape of the experimental EQE spectrum (open circles) is essentially similar to those of the CIGSe and CZTSe solar cells, although the longer λ response is limited in the CdTe solar cell due to a higher Eg (1.5 eV). In Fig. 2.21a, the red line represents the EQE spectrum calculated from the e-ARC method, while the EQE spectrum of LC = ∞ is indicated by the yellow-colored region. For this EQE analysis, the optical model of MgF2 (110 nm)/glass/ITO (200 nm)/CdS (50 nm)/CdTe (3.5 μm)/carbon electrode was

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Fig. 2.21 a Experimental EQE spectrum (open circles) of a CdTe solar cell consisting of MgF2/ glass/ITO (200 nm)/CdS (50 nm)/CdTe (3.5 μm)/carbon electrode [71], together with the fitted EQE result (red line) obtained from the e-ARC method assuming LC = 1.1 μm and b optical gain and loss obtained from the analysis [18]. In a, the absorptance spectra of the solar-cell component layers and RARC are also shown by the black lines. In b, the numerical values show the corresponding current densities in units of mA/cm2

constructed by referring to the description of [71]. The EQE calculation was implemented using the reported optical constants of MgF2 (Fig. 13.10), glass (Fig. 13.1), ITO (Fig. 11.18), CdS [16, 74], CdTe [75], and carbon (Fig. 12.9). In the EQE fitting analysis, only LC and the free carrier absorption in the ITO layer (i.e., AD) were adjusted. The AD value can be optimized rather easily from the EQE values at λ = 600–700 nm and the parameters of AD = 1.20 eV and Γ = 0.12 eV were used in the actual analysis, which correspond to the optical carrier concentration and mobility of Nopt = 2.4 × 1020 cm−3 and μopt = 35 cm2/(Vs), respectively [see (18.23)–(18.24) in Vol. 1]. It can be seen from Fig. 2.21a that the calculated EQE spectrum shows remarkable agreement with the experimental spectrum when LC = 1.1 μm. On the other hand, the experimental EQE is slightly smaller than the calculated EQE in a region of λ = 520–570 nm, indicating the small carrier loss near the CdS/ CdTe interface. It has been well established that a CdSxTe1-x alloy is formed at the CdS/CdTe interface [72, 76]. Thus, the slight EQE reduction suggests the carrier recombination within the CdSTe phase. Moreover, the disagreement observed at λ > 850 nm originates from the effect of the tail-state absorption. Although polycrystalline CdTe layers are expected to show tail absorption, the CdTe dielectric function extracted from a single crystal [75] was used in the analysis of Fig. 2.21a and the calculated EQE becomes smaller at λ > 850 nm. In Fig. 2.21b, the CdTe solar cell shows a high optical gain of ∼80%. It is noteworthy that the reflection loss and the absorption loss in the ITO layer ( 730 nm is caused by the insufficient modeling of the tail-state absorption. It should be emphasized that the similar good fitting can also be obtained when the a-Si:H i layer thickness is varied. Thus, once the parameter value of s (or αeff) is determined for a specific textured structure, the EQE characterization can be made rather easily. On the other hand, if the original α spectrum shown in Fig. 2.22b is applied, the calculated EQE spectrum (dotted line) deviates at λ > 625 nm and Jsc is underestimated by ∼1 mA/cm2. Thus, the approximated EQE characterization can still be made by using the ERC method. In the above analysis, since the EQE response in the longer λ region was

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Fig. 2.23 EQE analysis result and optical loss (gain) of the analyzed a-Si:H solar cell. The open circles show the experimental EQE spectrum, whereas the black lines indicate the RERS and absorptance spectra. The red line and black dotted line represent the EQE spectra calculated using the αeff and α spectra shown in Fig. 2.22b, respectively

adjusted, the determination of the recombination loss is difficult. The Jsc loss in the a-Si:H solar cell is attributed mainly to the reflection loss and the absorption loss in the front TCO layer. The relatively large reflection loss (∼4 mA/cm2) originates from the thin a-Si:H layer and the rather small α of a-Si:H. Because the a-Si:H solar cell is a superstrate-type solar cell, the thick SnO2:F layer is used and the absorption loss in this TCO is relatively large. In contrast, the optical loss in the rear structure (μc-Si:H/ZnO:Al/Ag) is well suppressed. As a result, the optical gain of the a-Si:H solar cell shows a value of ∼60%.

2.5

EQE Analysis of Textured c-Si Solar Cells

All the EQE analysis methods described above cannot be applied for solar cells having thick substrates ( ≥ 10 μm) as the optical response in this case needs to be calculated under the incoherent condition (Sect. 2.2.2). Since c-Si-based solar cells are generally formed using thick c-Si wafers (∼150 μm), the effect of the incoherent light absorption should be taken into account in the analysis of c-Si solar cells. However, it has been established that the coherent optical-admittance calculation can be extended to the calculation of incoherent optical systems with thick wafers by modifying the phase of propagating light waves [84]. This section introduces a new calculation scheme developed for the EQE analysis of various c-Si solar cells. It will be shown that even textured c-Si solar cells can be characterized from this method [84].

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2.5.1

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Continuous Phase Approximation

The calculation procedure of a coherent/incoherent optical system has long been established for the Fresnel approach (transfer matrix method) [85–87]. By adopting this calculation procedure [86, 87], a quite general calculation scheme, the continuous phase approximation (CPA) method, has been developed within the framework of the optical-admittance method [84]. In this section, this new procedure is introduced. As described above (Sect. 2.2.2), when the thickness of layers (or substrates) exceeds the coherent length of the incoming light, the phase information (i.e., δ expressed by (2.10)) is lost and the optical interference disappears. In the CPA method, the phase δ is varied intentionally so that the coherent optical response is eliminated [86, 87]. Figure 2.24 schematically explains the CPA method. In this figure, the propagation of the incident light in a thick incoherent layer, sandwiched by coherent layers, is illustrated. The slight attenuation of the wave amplitude reflects the light absorption within the incoherent layer. In the optical admittance method, the absorptance of the layer is calculated from ψ (Sect. 2.2.1). However, if ψ of the thick incoherent layer is calculated by applying (2.23), a very sharp interference pattern is generated by the terms cosδ and sinδ. In the CPA method, to remove the interference fringes, we change δ sequentially: δk =

2πNd k + π, λ m

ð2:39Þ

where the second term kπ/m shows the additional phase introduced to (2.10). In (2.39), m is a total number of the assumed waves, and k is the sequential number of the individual wave (k = 0, 1, …, m − 1). As illustrated in Fig. 2.24, when the phase is changed, the peak and valley positions of the incident wave show a shift. Thus, if all the waves are integrated, the interference effect can be eliminated. In the actual calculation, ψ of each wave (i.e., ψ(δk)) is obtained first and, by modifying (2.26), the absorptance of the jth incoherent layer (Ainc,j) is determined as follow [84]: Ainc, j =

j−1 1 m−1 ∑ ð1 − Rflat Þ½1 − ψ ðδk Þ ∏ ψ n m k=0 n=1 j−1

ð2:40Þ

= ð1 − Rflat Þð1 − ψ eff Þ ∏ ψ n , n=1

where ψ eff shows the effective ψ of the incoherent layer given by ψ eff =

1 m−1 ∑ ψ ðδk Þ. m k=0

ð2:41Þ

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Fig. 2.24 Principle of the continuous phase approximation (CPA) method used for the calculation of solar cells with thick substrates. In this method, ψ is calculated for various δk given by (2.39) and the effective ψ (ψ eff) is then obtained as an average of ψ(δk)

Thus, ψ eff is a simple average of different ψ(δk) values. Note that ψ(δ0) corresponds to ψ obtained from (2.23). The above calculation procedure can be incorporated into the ARC and ERS (or e-ARC and e-ERS) methods quite easily and, based on the above procedure, we can calculate the optical response of a complex multilayer structure, in which coherent and incoherent layers are mixed [84]. The reflectance spectrum of the incoherent optical model can also be calculated by modifying (2.18). Specifically, in this case, we first calculate Y0(δk), from which the reflectance of the flat structure is calculated by



1 m − 1

1 − Y0 ðδk Þ

2 ∑ , RCPA = m k = 0 1 + Y0 ðδk Þ

ð2:42Þ

where RCPA shows the reflectance obtained by applying the CPA method [84].

2.5.2

Analysis of Flat c-Si Solar Cells

Here, the EQE analysis of a flat c-Si heterojunction solar cell is described, as an example of the CPA calculation. In the analyzed c-Si solar cell [88], hydrogenated amorphous silicon oxide (a-SiO:H) layers are formed on both sides of the c-Si substrate (Sect. 9.1 in Vol. 1) with a structure of ITO (70 nm)/a-SiO:H p layer (3 nm)/a-SiO:H i layer (4 nm)/c-Si (300 μm)/a-SiO:H i layer (5 nm)/a-SiO:H n layer (15 nm)/ITO (70 nm)/Al. The conversion efficiency of this flat solar cell is 17.5% (Voc = 656 mV, FF = 0.75, Jsc = 35.6 mA/cm2). The O content in the a-SiO:H i layer is 4 at.%, whereas that of the p-n layers is 7 at.%. From these O contents, the dielectric functions of the a-SiO:H layers can be calculated using the model parameters shown

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in Fig. 9.16 (Vol. 1) [89], whereas the optical constants of the c-Si (Fig. 8.1), ITO (Fig. 11.4) and Al (Fig. 12.7) are shown in Part II of this book. Figure 2.25 shows the EQE spectrum calculated for the a-SiO:H/c-Si heterojunction solar cell. In this analysis, the absorptance of the c-Si substrate was calculated from (2.40) using m = 13. By assuming 100% carrier collection, the EQE spectrum was then obtained directly from the c-Si absorptance spectrum. In Fig. 2.25, the EQE spectra calculated for selected δk values (i.e., k = 0, 1, 2 and 12) are also shown. When a fixed δk is used, quite sharp interference fringes appear in the calculated EQE spectrum particularly in a low α region of c-Si. As confirmed from this figure, the interference pattern changes systematically with δk. The red line in Fig. 2.25 represents the EQE spectrum calculated from the CPA method. It can be seen that the optical interference effect induced by the c-Si is suppressed completely in the calculated spectrum. For the choice of m, the prime number is more preferable to eliminate the optical interference effectively when the m value is small. Figure 2.26a shows the result of the EQE analysis performed for the a-SiO:H/c-Si solar cell. The open circles denote the experimental data of [88], where the black and red lines show the CPA-derived absorptance and EQE spectra, respectively. The calculated EQE spectrum, which is consistent with that in Fig. 2.25, shows the remarkable agreement with the experimental EQE spectrum in the wide λ region and Jsc obtained from the calculation (35.0 mA/cm2) also agrees well with the experimental Jsc (35.4 mA/cm2). The result of Fig. 2.26a reveals that the a-SiO:H layers are “dead layers” that allow negligible carrier extraction. In the a-SiO:H/c-Si solar cell, the parasitic light absorption in the front TCO layer is relatively large (1.3 mA/cm2), while the optical loss in the rear structure (i.e., a-SiO:H(i-n)/ITO/Al)

Fig. 2.25 EQE spectra calculated for the a-SiO:H/c-Si heterojunction solar cell fabricated using a flat c-Si substrate. For the EQE spectra obtained using fixed δk values, only the results for k = 0, 1, 2 and 12 (m = 13) are shown for clarity. The red line represents the EQE spectrum calculated by applying the CPA method. The enlarged spectra in the range of 1000 < λ < 1100 nm are also shown

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Fig. 2.26 a Experimental EQE spectrum (open circles) of the a-SiO:H/c-Si heterojunction solar cell having a flat structure of ITO (70 nm)/a-SiO:H p layer (3 nm)/a-SiO:H i layer (4 nm)/c-Si (300 μm)/a-SiO:H i layer (5 nm)/a-SiO:H n layer (15 nm)/ITO (70 nm)/Ag [88], together with the calculated EQE result (red line) obtained from the CPA method and b EQE analysis results obtained for a-SiO:H/c-Si heterojunction solar cells with different c-Si wafer thicknesses (54– 300 μm) [88]. In a, the absorptance spectra of the solar-cell component layers and RCPA are shown by the black lines

is small (0.4 mA/cm2). Due to the flat structure, however, the reflection loss (8.8 mA/cm2) shows the largest contribution to the current loss in the a-SiO:H/c-Si solar cell. Figure 2.26b summarizes the results of the EQE analyses performed for similar a-SiO:H/c-Si heterojunction solar cells but with different c-Si thicknesses (54– 300 μm), reported in [88]. The EQE characterization result for the 300-μm-thick substrate corresponds to that shown in Fig. 2.26a. It can be seen that the calculation results are quite consistent with the experimental EQE spectra. Thus, the carrier recombination is quite small in these solar cells. By the increase in the c-Si wafer thickness, the EQE response in the longer λ region extends gradually, increasing Jsc from 33.3 mA/cm2 (54 μm) to 35.4 mA/cm2 (300 μm). It should be emphasized that, when the c-Si substrate is thinner, accuracy of the c-Si optical constants becomes quite important to obtain good matching with the experimental result. The excellent overall agreement confirmed in Fig. 2.26b justifies the c-Si optical constants used in the calculation (see Fig. 8.2 in Vol. 1 and Table 8.2 in Vol. 2). The results of Fig. 2.26 demonstrate that EQE analysis of solar cells with incoherent optical responses can be implemented rather easily by applying the CPA method. This calculation scheme can further be applied for the calculation of multi-junction solar cells consisting of group III–V compound semiconductors. Figure 2.27 shows the normalized partial EQE (absorptance) for the different depths from the a-SiO:H(i)/c-Si interface and wavelengths, obtained from the analysis of Fig. 2.26a. Unlike Figs. 2.12b and 2.17b, the partial EQE values in this

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Fig. 2.27 Normalized partial EQE (absorptance) for the different depths from the a-SiO:H(i)/c-Si interface and wavelengths, and integrated Jsc toward depth. Note that the partial EQE values are indicated by the logarithmic scale. The results in this figure are consistent with the EQE analysis result of Fig. 2.26a

figure are shown using the logarithmic scale due to the very small α values of indirect-transition c-Si in the longer λ region (see Fig. 1.6). As shown in Fig. 2.27, the carrier generation is rather uniform up to 5 μm but the light absorption continues to occur even at 300 μm in the long λ region of 900 ≤ λ ≤ 1200 nm. In Fig. 2.27, the calculation result of Jsc for the depth is also shown. As confirmed from this result, Jsc increases to ∼24 mA/cm2 at the depth of 10 μm, followed by the gradual increase observed at the depth of d >10 μm. For c-Si solar cells, to suppress the wafer cost, the use of thinner Si wafers is quite favorable. In this case, however, Jsc of the solar cells simply decreases as the light absorption becomes more difficult. To suppress the Jsc reduction observed in thinner c-Si solar cells, the efficient optical confinement is crucial.

2.5.3

Analysis of Textured c-Si Solar Cells

Rather surprisingly, the EQE analysis of textured c-Si solar cells can be performed by adopting the above calculation procedure [84]. In general, for the fabrication of c-Si solar cells, pyramid-shaped textures (see Fig. 4.1) are widely employed. As described in Sect. 4.2.4, the optical response of thin layer structures formed on the c-Si textures can be described using the coherent condition and the light scattering effect within the thin layers is very small. Furthermore, due to the shape of the specific c-Si texture, the transmission angle of the incident light in the thin film structure is close to the normal to the {111} texture-facet plane. More specifically,

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the optical characterization described in Sect. 4.2.2 confirms that the top angle of the pyramid-shaped texture is 80o (see also Fig. 4.5) and the incident angle for the {111} facet is 50°, as illustrated in Fig. 2.28. Since the refractive indices of the ITO, a-Si:H and c-Si at λ = 1100 nm are n = 1.7 (Table 11.8), n = 3.6 (Table 8.21), and n = 3.5 (Table 8.2), the transmission angles become 27°, 12° and 12°, respectively. Consequently, the absorptance of the TCO and a-Si:H layers can be approximated assuming the normal incidence in the coherent optical model [84]. More importantly, if the suppressed light reflection by the c-Si texture is expressed by the ERS method, the light absorption in the whole structure can be deduced using a completely flat optical model [84]. The above calculation procedure for textured c-Si solar cells is exactly the same as that described in the previous section but only the experimental reflectance spectrum is used in this case to incorporate the texture effect. Figure 2.29a shows an optical model constructed for a textured a-Si:H/c-Si heterojunction solar cell reported in [90]. This solar cell has a structure of ITO/a-Si: H(p)/a-Si:H(i)/c-Si/a-Si:H(i)/a-Si:H(n)/ITO/Ag. For the EQE analysis, the layer thicknesses described in [90] were adopted, but the thicknesses of the a-Si:H p-i layers were reduced to half to obtain good agreement with the experimental result. In Fig. 2.29a, the layer thicknesses used in the actual analysis are summarized. For the optical constants of the component layers, the optical spectra of a-Si:H p and i layers [11] and an ITO layer with a carrier concentration of 2.4 × 1020 cm−3 [12], reported by the same research group, were employed, while the optical constants of Fig. 8.1 were used for the c-Si. In addition, the optical constants of the a-Si:H n layer was assumed to be identical to those of the a-Si:H i layer. Figure 2.29b shows the EQE analysis result obtained for the a-Si:H/c-Si heterojunction solar cell based on the ERS-CPA approach. It can be seen that, even

Fig. 2.28 Optical transmission in a TCO/a-Si:H thin film structure formed on a pyramid-shaped c-Si texture. The top angle of the c-Si texture is 80° (see Fig. 4.5) and the transmission angles are calculated assuming n = 1.7 (ITO: Table 11.8), n = 3.6 (a-Si:H: Table 8.21) and n = 3.5 (c-Si: Table 8.2) at λ = 1100 nm. As a result, the transmission angle is close to the normal to the {111} texture-facet plane

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Fig. 2.29 a Optical model constructed for a reported a-Si:H/c-Si heterojunction solar cell [90] and b EQE analysis result obtained for the a-Si:H/c-Si heterojunction solar cell using the ERS-CPA method. In a, the current density loss (Jloss) and Jsc determined from the analysis are also shown. In b, the experimental reflectance and EQE spectra (open circles) and the calculated EQE and absorptance spectra (red and black lines) are indicated

though the quite simple calculation scheme has been applied, the calculated EQE spectrum (red line) shows remarkable agreement with the experimental spectrum (open circles). As mentioned above, the a-Si:H p-i layer thickness were reduced, compared with the reported thicknesses, since otherwise the calculated EQE values become notably lower than the experimental EQE values in the short λ region of 300 ≤ λ ≤ 600 nm. In other words, the effective thicknesses of the a-Si:H p-i layers can be deduced rather easily from the EQE analysis assuming no carrier extraction from the a-Si:H layers [84] as observed in Fig. 2.26a. The black lines in Fig. 2.29b show the absorptance spectra of the solar-cell component layers and the optical losses (gain) estimated from these spectra are also indicated in Fig. 2.29a. In the a-Si:H/c-Si heterojunction solar cells, the parasitic absorption in the a-Si:H p-i layers is relatively large (see also Fig. 9.7 in Vol. 1) and the ITO layer also induces the optical loss, but the optical gain is quite high (85.6%). However, it should be noted that Jsc obtained from the reported EQE spectrum of [90] (40 mA/cm2) is higher than ∼37 mA/cm2 determined from the current density-voltage measurement [90] because the shadow loss of the front electrode is not considered in EQE.

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Carrier Loss Mechanisms

In this section, from the above EQE analysis results, the carrier loss mechanisms in various solar cells are discussed. It will be emphasized that the carrier recombination is affected by not only defect creation but also the light absorption characteristics of the absorber layers.

2.6.1

Effect of Carrier Collection Length on Jsc

Figure 2.30a summarizes the α spectra of the various light absorbers applied for the above EQE analyses [18]. The α spectrum of the CH3NH3PbI3 hybrid perovskite is also shown for comparison. In this figure, all the semiconductors show α ∼104 cm−1 near the Eg region. However, for CdTe and CH3NH3PbI3, quite sharp absorption edges can be confirmed, whereas the kesterite compounds (i.e., CZTSe and CZTS) exhibit a broad optical transition near the Eg region (see Fig. 1.6). Quite importantly, the near-Eg absorption characteristics affect the carrier recombination behavior rather significantly. To understand this behavior quantitatively, the EQE simulations have been performed for the solar cell materials of Fig. 2.30a. Figure 2.30b shows the variation of Jsc with LC calculated from the e-ARC method [18]. For all the solar cells, an identical solar cell structure consisting of

Fig. 2.30 a α spectra of the various light absorbers applied for the EQE analyses and b variation of Jsc with LC calculated from the e-ARC method [18]. The optical data of a show reported values of CZTSe (Fig. 8.30), CZTS (Fig. 8.29), CISe (Fig. 8.24), CdTe [75], CH3NH3PbI3 (Fig. 10.2) and CGSe (Fig. 8.25). In b, a fixed layer thickness of 2 μm is assumed

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MgF2 (130 nm)/ZnO:Al (360 nm)/ZnO (50 nm)/CdS (45 nm)/absorber (2.0 μm)/ Mo was assumed, except for CdTe and CH3NH3PbI3 solar cells. For these solar cells, the structures of Fig. 2.21 (CdTe) and Fig. 16.17 in Vol. 1 (CH3NH3PbI3) were adopted, but the calculations were implemented using an identical absorber thickness of 2.0 μm. For the simulations of CZTSe and CZTS solar cells, the Eg values are increased slightly: i.e., Eg = 1.0 eV (CZTSe) and Eg = 1.45 eV (CZTS) based on the result of Fig. 2.19. In Fig. 2.30b, Jsc is higher in the solar cell with a low-Eg absorber and Jsc increases rapidly with increasing LC. The variations of Jsc with LC are essentially similar in all the solar cells and Jsc tends to saturate at LC >1.0 μm because α of the absorbers is ∼104 cm−1 and the resulting dp is ∼1 μm (Fig. 1.11b). Nevertheless, the Jsc values of the CdTe and CH3NH3PbI3 solar cells show almost complete saturation at LC >1.0 μm. This trend originates from the sharp absorption features of these absorbers. As a result, in CdTe and CH3NH3PbI3 solar cells, JscJsc is not influenced by the recombination as long as the condition of LC >1.0 μm is satisfied. The suppressed carrier recombination in CdTe can be understood more visually from the partial absorptance. Figure 2.31 shows the partial absorptance of (a) CdTe and (b) CZTSe solar cells calculated in the simulation of Fig. 2.30b [18]. It can be seen that the carrier generation in the CdTe layer occurs more uniformly in the depth direction, compared with the CZTSe layer. This arises from the smaller penetration depth of light in the longer λ region due to higher α values. In particular, because of the sharp absorption edge of the CdTe, most of the light is absorbed in the region quite close to the CdS/CdTe interface. Thus, even when LC is rather small (LC ∼1 μm), the carrier loss occurs only in a limited λ region of 800–850 nm (Fig. 2.31a). As a result, the influence of the carrier recombination is suppressed quite well in the CdTe solar cell. In fact, rather surprisingly, LC of the CdTe solar cell (∼1 μm in Fig. 2.21) is comparable to those of the CZTSe and CZTS solar cells

Fig. 2.31 Partial absorptance of a CdTe and b CZTSe solar cells calculated in the simulation of Fig. 2.30b [18]. The partial absorptance values are normalized by the maximum values obtained in each solar cell

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(∼1 μm in Fig. 2.18), even though the carrier recombination loss in the CdTe solar cell is quite small (1.0 mA/cm2 in Fig. 2.21), compared with that in the CZTSe (∼6 mA/cm2 in Fig. 2.15). Accordingly, carrier recombination is influenced significantly by the α spectrum of a light absorber layer and the recombination loss decreases, if α(λ) shows high values with sharp absorption edge (or a low Urbach energy). In this sense, α(λ) of CdTe and CH3NH3PbI3 has a more ideal shape, if compared with CZTSe and CZTS.

2.6.2

Carrier Loss in Various Solar Cells

Table 2.1 summarizes Jsc, the optical loss and recombination loss of the various solar cells, determined from the EQE analyses in this chapter and Chap. 16 in Vol. 1. In this table, the results are ordered by decreasing Eg of the solar-cell absorber layer, and the optical gains of each solar cell are also indicated. Unfortunately, for many record efficiency solar cells, the detailed structures and optical properties of the component layers are not clear and the EQE analyses are not possible. Thus, the carrier losses and gains summarized in Table 2.1 represent reference values and the best-performing solar cells may exhibit more suppressed Jsc losses. For all thin-film solar cells and c-Si heterojunction solar cells, the current losses induced by the reflection and the parasitic absorption in a front TCO layer are common problems. Although the wide-Eg a-Si:H and hybrid perovskite (CH3NH3PbI3) solar cells exhibit the large reflection and TCO absorption losses, these optical losses tend to increase in solar cells having low-Eg absorbers due to the widening of the EQE spectral range. In fact, the reflection loss of the wide-gap CdTe solar cell is less than 1 mA/cm2, while those of the CZTSe and CZTSSe solar cells are quite large (2.5–4.5 mA/cm2). When low-Eg absorbers are applied, therefore, the suppression of the reflection loss and absorption loss in the front TCO becomes critical in achieving high conversion efficiencies. The high reflection losses observed in the wide-Eg a-Si:H and CH3NH3PbI3 solar cells are caused by the quite thin absorber layers (200–300 nm). As confirmed from Table 2.1, the Jsc loss induced by the TCO parasitic absorption reduces the optical gain notably. For example, Al-doped ZnO layers (∼350 nm) with a carrier concentration of ∼2 × 1020 cm−3 result in the absorption loss of ∼3 mA/cm2 (see Figs. 2.11b and 2.15b). In the CZTSSe solar cell shown in Table 2.1, the TCO absorption is suppressed by incorporating a thin ITO layer (50 nm) [14]. In the CdTe solar cell, the optical loss caused by the front ITO is only 0.7 mA/cm2 even though the ITO thickness is 200 nm. This small optical loss in the front TCO originates from the large Eg value of CdTe, which limits the effect of the free carrier absorption, as the free carrier absorption in TCO layers increases drastically at longer wavelengths (Fig. 18.8 in Vol. 1). In contrast, the a-Si:H and CH3NH3PbI3 solar cells having larger Eg show the relatively large front TCO losses. This is caused by strong free carrier absorption originating from a thick TCO

Jsc (mA/cm2)

Optical loss (mA/cm2) Reflection loss TCO Doped layer

Metal

Recombination loss (mA/cm2)

Optical gain (%)

Analysis

a-Si:H 15.0 3.7 3.6 1.0 0.7 – 63 Fig. 2.23 3.2 3.4 0.1a 0.6 0.9 70 Fig. 16.19 (Vol. 1) CH3NH3PbI3 18.7 0.5 1.0 79 Fig. 2.21 CdTe 24.5 0.9 0.7 3.3b 8.3c 1.4 51 [18] CZTS 20.2 1.2 4.4 4.1b 3.2 0.0 78 Fig. 2.11 CIGSe 34.0 1.2 2.8 2.5b 1.9 2.7 1.4e 0.7 0.0 86d Fig. 2.29 a-Si:H/c-Si 39.8 d b c 3.8 5.2 68 Fig. 1.14 CZTSSe 35.4 4.5 1.4 1.8 4.6c 6.5 61 Fig. 2.15 CZTSe 31.6 2.5 3.5 3.5b a Total optical loss in the electron and hole transport layers, bOptical loss induced by the n-type CdS layer, cTotal optical loss of the Mo and Mo(S)Se2 layers, d Jsc without the front electrode, eTotal optical loss of the a-Si:H p-i layers

Solar cell

Table 2.1 Jsc, optical loss and recombination loss of various solar cells determined from the EQE analyses. The results are ordered by decreasing Eg of the solar-cell absorber layer, and the optical gains of each solar cell are also indicated. For the optical losses of the TCO, doped and metal layers, the total losses obtained by summing the contributions of related layers are indicated

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layer (600–900 nm) with a high carrier concentration of (3–5) × 1020 cm−3 (Asahi-U and TEC-8 substrates: see Table 18.2 in Vol. 1). The parasitic light absorption in the front TCO can be reduced by employing high-mobility TCO layers, which exhibit quite low free carrier absorption (Chap. 19 in Vol. 1). In the CIGSe, CZTSe, CZTS and CdTe solar cells, the optical loss induced by the n-type doped CdS layer (∼50 nm) is ∼3 mA/cm2. In the CZTSSe solar cell, the optical loss in the CdS layer is reduced by incorporating a quite thin CdS layer (25 nm) [14]. In high-efficiency CdTe solar cells, the parasitic absorption in the CdS layer is also reduced by adopting a thin layer [77, 78], as mentioned earlier. For CIGSe solar cells, to suppress the Jsc loss induced by the CdS layer, a Zn(O,S) layer has also been applied [91]. In the CIGSe and CZTSSe-based solar cells, a strong optical loss also occurs by the parasitic absorption in the Mo layer. This effect can be attributed to the very low reflectance of Mo, as mentioned above (Fig. 12.4). The strong parasitic absorption in the Mo is evident in the EQE analysis results for the CIGSe and CZTSe solar cells (Figs. 2.11a and 2.15a). In contrast, quite high reflectance can be obtained in the a-Si:H, CH3NH3PbI3 and c-Si solar cells, which employ Al, Ag, and Au back reflectors (Fig. 12.3). Accordingly, in the Cu-Se containing semiconductors, the parasitic absorption by the CdS and Mo layers causes the large Jsc reduction. It should be emphasized that the CH3NH3PbI3 and CdTe solar cells show small overall optical losses. In particular, the parasitic absorption within the electron and hole transport layers in the hybrid perovskite solar cell is negligible (only 0.1 mA/ cm2 in Table 2.1) and the major absorption loss occurs only in the front TCO layer. Thus, a quite high conversion efficiency reported for CH3NH3PbI3 solar cells (∼20%) can be understood in part by the low parasitic absorption within the solar-cell component layers [17, 18]. In the CIGSe and a-Si:H/c-Si heterojunction solar cells, the recombination loss is negligible and high optical gains of ∼80% have been realized. All the other solar cells show the recombination losses, primarily because of the lack of the BSF structures in the solar cells. The results of Table 2.1 show clearly that the reduction of the optical and recombination losses is critical in achieving high conversion efficiencies. For the determination of the performance-limiting optical and physical factors in solar cells, the EQE analysis described in this chapter provides a fast and reliable method.

2.7

Free Software for EQE Analysis

A window-based free computer software (e-ARC software), which can be applied to the EQE analysis and simulation described in this chapter, was released at EU-PVSC conference (Amsterdam, Sept. 25 in 2017) and can be downloaded from a web site (https://unit.aist.go.jp/rcpv/cie/service/index.html). Figure 2.32 shows the computer screen of the e-ARC software. In this figure, the analysis example of the CIGSe solar cell described in Sect. 2.2.3 is shown. In this software, the EQE

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Fig. 2.32 Computer screen of the EQE analysis program (e-ARC software). The analysis example for a CIGSe solar cell is shown. This free software can be downloaded from a web site (https:// unit.aist.go.jp/rcpv/cie/service/index.html)

calculation can be finished within a second. The software is quite easy to operate and is recommended particularly for students and researchers who intend to optimize solar cells.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

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Chapter 3

Optical Simulation of External Quantum Efficiency Spectra Prakash Koirala, Abdel-Rahman A. Ibdah, Puruswottam Aryal, Puja Pradhan, Zhiquan Huang, Nikolas J. Podraza, Sylvain Marsillac and Robert W. Collins Abstract Applications of ex situ spectroscopic ellipsometry (SE) are presented for determination of the parameters that describe the dielectric function and structure of thin film solar cells. Complete optical models of solar cells developed using least squares regression analysis of the SE data enable external quantum efficiency (EQE) simulations for comparison with measurements. Through this comparison, it becomes possible to understand in detail the origins of optical and electronic collection and losses in thin film photovoltaics technologies and, as a result, the underlying performance limitations. Examples of this approach are presented for the three commercialized thin film technologies of hydrogenated amorphous silicon (a-Si:H), cadmium telluride (CdTe), and copper indium-gallium diselenide (CuIn1–xGaxSe2; CIGS). In the studies of a-Si:H solar cells, a comparison between the EQE simulation based on the SE model and the measured EQE suggests electrical losses from photo-generated carriers near the p/i and i/n interfaces, the latter caused by an i-layer thickness greater than the hole collection length. Also demonstrated here through comparisons of EQE measurements and simulation is enhanced carrier collection near the p/i interface when a protocrystalline Si:H i-layer of improved electrical quality is incorporated at the interface. For a CdS/CdTe heterojunction solar cell in the superstrate configuration, SE is performed through the glass, and simulations of the EQE spectra have been generated on the basis of comprehensive optical property and multilayer analysis by SE. In this case, observed deviations between simulated and measured EQE can assist in refining the optical model of the cell. Applying these methods, the optical losses that occur when photons with above-bandgap energies are not absorbed within the cell’s active layers can be P. Koirala ⋅ A.-R. A. Ibdah ⋅ P. Aryal ⋅ P. Pradhan ⋅ Z. Huang ⋅ N. J. Podraza (✉) R. W. Collins Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH 43606, USA e-mail: [email protected] R. W. Collins e-mail: [email protected] S. Marsillac Virginia Institute of Photovoltaics, Old Dominion University, Norfolk, VA 23529, USA © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_3

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distinguished from electronic losses that occur when electrons and holes photo-generated within these active layers are not collected. CIGS/CdS heterojunction solar cells incorporating both standard thickness and thin absorbers are also studied using SE. Data analysis is more challenging for CIGS because of the need to extract absorber layer Ga profiles for accurate optical models. For cells with standard thickness absorbers, excellent agreement is found between the simulated and measured EQE, the latter under the assumption of 100% collection from the active layers. For cells with thin absorbers, however, the difference observed between the simulated and measured EQE can be assigned to losses via electron-hole recombination near the Mo back contact. When a probability profile for carrier collection is introduced into the EQE simulation, closer agreement between this simulation and the measurement is observed. In addition to a single spot capability of SE as presented in this study, a capability also exists for high resolution mapping of multilayer thicknesses and component layer characteristics that provide short-circuit current density predictions. The mapping capability is made possible due to the high speeds [ 3 × 105 cm−1) below the band gap of CIGS

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generates a change in ψ(t) sufficient for detection of the transitions. Basically, as more heavily absorbing Cu2−xSe accumulates on the surface of the CIGS bulk layer, the interference fringe pattern associated with this layer will shift in photon energy and the pattern envelope will dampen in amplitude. Even when a thick roughness layer exists on the CIGS surface, the time evolution of the real time SE data in ψ exhibit features at the transitions from Cu-poor to Cu-rich CIGS and from Cu-rich to Cu-poor CIGS. These transitions can be identified with greater sensitivity from the time derivative dψ/dt in Fig. 6.30 [5]. For photon energies lower than the band gap of CIGS, the suppression and enhancement of optical interference amplitudes associated with the growing bulk layer pinpoints the two transitions. Considering the evolution of dψ/dt, the sequence of two transitions generates a decrease in oscillations of the derivative toward zero and an increase in these oscillations above zero. The large changes in dψ/dt after the Cu-rich to Cu-poor transition near 71 min are generated by the interference fringe shift caused simply by an increase in the CIGS bulk layer thickness in the Cu-poor stage of film growth. The times associated with these optically detected transitions correlate with those at which variations in the substrate heater power occur, as shown in Fig. 6.30 (top panel). The indirect measurement of film surface emissivity through the heater power could not be applied to the deposition on the c-Si wafer substrate in Fig. 6.29 due to the thin CIGS layer and the thermal characteristics of the substrate. The results in Fig. 6.30 demonstrate the application of real time SE as a process monitor as well as for process control of three-stage CIGS deposition. This capability has been used to supplement the conventional approaches, and because of the enhanced information content provided by in-depth real time SE analysis, ultimately it may be used in the future to replace the conventional approaches [30].

6.5

Summary

Real time SE has been implemented for in situ analysis and monitoring of the three coevaporation stages applied in optimized deposition processes for CuIn1−xGaxSe2 (CIGS) thin films. These films are employed as absorber layer components incorporated into high efficiency CIGS photovoltaic devices [5–8]. Stage I of the deposition process entails coevaporation of In, Ga, and Se onto an opaque Mo-coated soda lime glass substrate held at a temperature of ∼400 °C, yielding an (In1−xGax)2Se3 (IGS) thin film. From real time SE, the evolution of the structure of the IGS film in terms of the thicknesses of the bulk and surface roughness layers can be determined as well as the final composition of the IGS film. During stage II, coevaporation of Cu and Se converts the IGS film to CIGS. A model of uniform conversion throughout the bulk layer is substantiated for analysis of the real time SE data in stage II, resulting in time dependent and average conversion rates of IGS to CIGS in terms of layer thickness and component volume percentages. Before the stage II endpoint, the formation of a Cu2−xSe layer on the CIGS surface can be

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observed by real time SE and tracked in terms of its effective thickness or volume per substrate area and its rate of development. The Cu2−xSe effective thickness at the surface of the CIGS film is determined over a time interval extending from the stage II endpoint and through much of stage III. In this stage III, the Cu-rich CIGS film and the Cu2−xSe at the surface are converted through the coevaporation of In, Ga, and Se to a CIGS film that is slightly Cu-poor. Real time SE can be used to identify the transition from Cu-rich to Cu-poor CIGS. Results for a continuous process of CIGS deposition in which a substrate shutter is opened/closed only at the start/end of the entire three-stage deposition are compared with results in which the shutter is used additionally to separate the stages. Detailed differences in the real time SE analysis results for the two processes suggest possible reasons for the improved solar cell performance when shuttering is performed between stages. The three stages of the coevaporation process have been investigated in detail by applying real time SE to the fabrication of ∼2.2 and ∼0.3 μm thick CIGS absorber layers using a substrate shutter between stages. This analysis technique enables detailed comparison of the general features of the structural evolution, including grain growth and coalescence processes. Because real time SE enables determination of the IGS thickness and characterization of the phase conversions from IGS to CIGS and from Cu2−xSe to CIGS during the CIGS growth process, the analysis technique is shown to be capable of detecting the desired coevaporation endpoint in each of the three stages. Thus, this endpoint detection capability can be applied during the fabrication of the thin film absorber layer component for CIGS solar cells to complement previously-developed techniques. These techniques include electron impact emission spectroscopy (EIES) for measuring the elemental fluxes as well as pyrometry or substrate heater power monitoring for respective direct or indirect measurements of the emissivity of the film surface. The dielectric functions of the bulk IGS and CIGS layers, obtained from the real time SE analysis can provide further compositional fingerprints as well as compositional depth profiles assuming that an adequate database exists. Such a database has been developed for IGS as well as for CIGS and Cu2−xSe in previous work reviewed here. The composition analysis capabilities need further expansion and evaluation in future investigations. The unprocessed data obtained by real time SE has been applied as well to follow the transitions between Cu-rich and Cu-poor states of the CIGS film surface in stages II and III of CIGS coevaporation [5]. Such an application is of interest if one seeks instantaneous feedback. In fact, variations in the amount of Cu2−xSe on the CIGS film surface can be inferred not only from an in-depth analysis of (ψ, Δ) spectra versus time, but also directly from the time evolution of the ellipsometry angle ψ. Here the sensitivity of ψ(t) to the phase transition times was demonstrated for CIGS layers deposited on c-Si wafers and on Mo-coated glass. These transition times obtained from ψ(t) correlate well with those from conventional indirect measurements of the emissivity of the substrate/film. Thus, real time SE has been demonstrated as a monitor of the presence of Cu2−xSe on the CIGS surface and the phase transitions that CIGS absorbers undergo during three-stage coevaporation, both in test configurations and in the solar cell device configuration. The capabilities of this non-destructive, high speed thin film analysis technique are

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demonstrated for complementing or replacing existing monitoring and control techniques conventionally required for multi-stage coevaporation of CIGS in laboratory and industry applications. As a result, the technique provides insights enabling the optimization of materials and device structures as well as guidance enabling process control so that desired materials and device specifications can be met. In final summary, it has been demonstrated in this chapter that in situ real time SE combines high thickness, phase, and compositional sensitivity with fast non-invasive data acquisition, thus providing unique insights into the dynamics of CIGS film growth. The information extracted from real time SE includes the time evolution of thicknesses that characterize bulk and surface roughness layers, as well as the evolution of the phase composition of the layers. From this information, a better understanding of the CIGS growth process throughout the three stages of deposition can be obtained. Although the results of this real time SE analysis are found to be consistent with models proposed previously, real time SE provides insights into the origins of variations in cell performance that may occur due to variations in processing. This in-depth understanding can assist in evaluating the fabrication process and thus in further enhancing the performance of optimized thin film solar cells.

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10. A.M. Gabor, J.R. Tuttle, M.H. Bode, A. Franz, A.L. Tennant, M.A. Contreras, R. Noufi, D.G. Jensen, A.M. Hermann, Sol. Energy Mater. Sol. Cells 41–42, 247 (1996) 11. S. Marsillac, R.W. Collins, in Physics, Simulation, and Photonic Engineering of Photovoltaic Devices, San Francisco, CA, 23–26 January 2012, Conference Proceedings of SPIE, vol. 8256, ed. by A. Freundlich, J.-F.F. Guillemoles (SPIE, Bellingham, WA, 2012), Art. No. 825613, pp. 1–11 12. J. Li, R.W. Collins, M.N. Sestak, P. Koirala, N.J. Podraza, S. Marsillac, A.A. Rockett, in Advanced Characterization Techniques for Thin Film Solar Cells, 2nd edn., ed. by D. Abou-Ras, T. Kirchartz, U. Rau (Wiley-VCH, Weinheim, Germany, 2016), Chapter 9, pp. 215–256 13. J.D. Walker, H. Khatri, V. Ranjan, S. Little, R. Zartman, R.W. Collins, S. Marsillac, in Proceedings of the 34th IEEE Photovoltaic Specialists Conference, Philadelphia, PA, 7–12 June 2009 (IEEE, New York, NY, 2009), pp. 1154–1156 14. S. Marsillac, V. Ranjan, S. Little, R.W. Collins, in Proceedings of the 35th IEEE Photovoltaic Specialists Conference, Honolulu, HI, 20–25 June 2010 (IEEE, New York, NY, 2010), pp. 866–868 15. P. Aryal, A.-R. Ibdah, P. Pradhan, D. Attygalle, P. Koirala, N.J. Podraza, S. Marsillac, R.W. Collins, J. Li, Prog. Photovolt.: Res. Appl. 24, 1200 (2016) 16. Y. Cong, I. An, K. Vedam, R.W. Collins, Appl. Opt. 21, 2692 (1991) 17. I. An, Y.M. Li, H.V. Nguyen, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 59, 2543 (1991) 18. B. Johs, J.S. Hale, Phys. Stat. Solidi (a) 205, 715 (2008) 19. H. Fujiwara, J. Koh, P.I. Rovira, R.W. Collins, Phys. Rev. B 61, 10832 (2000) 20. J. Li, J. Chen, J.A. Zapien, N.J. Podraza, C. Chen, J. Drayton, A. Vasko, A. Gupta, S.L. Wang, R.W. Collins, A.D. Compaan, in Thin-film Compound Semiconductor Photovoltaics, Materials Research Society Symposium Proceedings, vol. 865, ed. by W. Shafarman, T. Gessert, S. Niki, S. Siebentritt (MRS, Warrendale, PA, 2005), Symposium F; F1.2.1, pp. 9–14 21. J. Li, J. Chen, M.N. Sestak, R.W. Collins, IEEE J. Photovolt. 1, 187 (2011) 22. T. Begou, J.D. Walker, D. Attygalle, V. Ranjan, R.W. Collins, S. Marsillac, Phys. Stat. Solidi RRL 5, 217 (2011) 23. J.D. Walker, H. Khatri, V. Ranjan, J. Li, R.W. Collins, S. Marsillac, Appl. Phys. Lett. 94, 141908 (2009) 24. J. Koh, A.S. Ferlauto, P.I. Rovira, R.J. Koval, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 75, 2286 (1999) 25. J.D. Walker, H. Khatri, S. Little, V. Ranjan, R. Collins, S. Marsillac, in Photovoltaic Materials and Manufacturing Issues II, Materials Research Society Symposium Proceedings, vol. 1210, ed. by B. Sopori, J. Yang, T. Surek, B. Dimmler (MRS, Warrendale, PA, 2009), Symposium Q; Q06-02, pp. 159–164 26. D.I. Chakrabarti, D.E. Laughlin, Bull. Alloy Phase Diagr. 2, 305 (1981) 27. V.M. Glazov, A.S. Pashinkin, V.A. Fedorov, Inorg. Mater. 36, 641 (2000) 28. P. Aryal, Optical and Photovoltaic Properties of Copper Indium-gallium Diselenide Materials and Solar Cells. Ph.D. Dissertation, (University of Toledo, Toledo, OH, 2014) 29. S. Marsillac, V. Ranjan, K. Aryal, S. Little, Y. Erkaya, G. Rajan, P. Boland, D. Attygalle, P. Aryal, P. Pradhan, R.W. Collins, in Proceedings of the 38th IEEE Photovoltaic Specialists Conference, Austin, TX, 3–8 June 2012 (IEEE, New York NY, 2012), pp. 1492–1494 30. J. Li, M. Contreras, J. Scharf, M. Young, T.E. Furtak, R. Noufi, D. Levi, in Proceedings of the 39th IEEE Photovoltaic Specialists Conference, Tampa, FL, 16–21 June 2013 (IEEE, New York, NY, 2013), pp. 2609–2611

Chapter 7

Real Time and Mapping Spectroscopic Ellipsometry of Hydrogenated Amorphous and Nanocrystalline Si Solar Cells Zhiquan Huang, Lila R. Dahal, Sylvain Marsillac, Nikolas J. Podraza and Robert W. Collins

Abstract Real time spectroscopic ellipsometry (SE) has been applied to characterize the structural evolution and optical properties of the critical p-type doped and intrinsic hydrogenated silicon (Si:H) layers that comprise the nanocrystalline Si:H bottom cell of tandem photovoltaic (PV) devices. The tandem PV devices under study are fabricated in the amorphous/nanocrystalline Si:H (a-Si:H/nc-Si:H) p-i-n superstrate configuration in which the nc-Si:H cell is at the bottom of the device structure due to its narrower bandgap relative to that of the top cell a-Si:H. SE data collected in real time during Si:H solar cell fabrication by plasma enhanced chemical vapor deposition (PECVD) enable identification of Si crystallite development in the bottom cell p and i-layers through the evolution of surface roughness, as well as through variations in the optical properties in the form of the complex dielectric function ðε = ε1 − iε2 Þ. Analysis of the dielectric function permits quantification of the relative amounts of the a-Si-H and nc-Si-H components that exist during the growth of mixed-phase Si:H layers. Based on these real time SE analysis results, a PECVD growth evolution diagram has been developed for the bottom cell i-layer of the tandem PV cell in order to guide fabrication in this device configuration. Correlations between the p and i-layer structures and device performance are evident and can be understood on the basis of the growth evolution diagram. A second growth evolution diagram has been developed to characterize PECVD of n-type Si-H thin films for use as the n-layer component of p-i-n a-Si:H top cells in the same superstrate configuration. This growth evolution diagram has been established to provide guidance for PECVD of the n-layers over the 15 cm × 15 cm areas of glass/TCO/p/i superstrates, where TCO represents the transparent conducting oxide layer serving as the topmost contact. The goal of this study is to Z. Huang ⋅ L. R. Dahal ⋅ N. J. Podraza (✉) ⋅ R. W. Collins Department of Physics & Astronomy and Center for Photovoltaics Innovation & Commercialization, University of Toledo, Toledo, OH 43606, USA e-mail: [email protected] S. Marsillac Virginia Institute of Photovoltaics, Old Dominion University, Norfolk, VA 23529, USA © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_7

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correlate the structural characteristics provided by the diagram with the performance parameters of single-junction a-Si:H solar cells that can serve as the top cell of the tandem device. A 16 × 16 array of p-i-n dot cells has been fabricated over the 15 cm × 15 cm area of the TCO coated glass superstrate, and this same area has been studied by mapping SE. Analysis of the SE data collected over the full area provides maps of the p-layer effective thickness, i-layer thickness and bandgap, and n-layer thickness and nanocrystalline volume fraction for spatial correlation with the performance parameters from current density-voltage (J-V) measurements of the 16 × 16 array of dot cells. The goal of the correlations that exploit mapping SE is to identify and understand the relationships between the variations in the basic materials properties and in the thin film solar cell performance over large areas. The results also enable analysis of the impacts of spatial non-uniformities on PV module performance.

7.1

Introduction and Overview

Hydrogenated amorphous silicon (a-Si:H) and hydrogenated nanocrystalline silicon (nc-Si:H) thin films fabricated by plasma enhanced chemical vapor deposition (PECVD) have been studied extensively for photovoltaics (PV) applications over many years [1, 2]. The doped forms of both a-Si:H and nc-Si:H exhibit high defect concentrations, and as a result, the solar cells based on these materials are fabricated in either p-i-n superstrate or n-i-p substrate configurations. Due to the lower mobility of holes, the light is passed first through the p-type hydrogenated Si (Si:H) (or p-layer), which serves as an inactive window layer of the cell in both configurations. As a result, these cells require a very thin Si:H p-layer having a wide bandgap in order to reduce collection losses due to absorption of photons in the inactive layer. Because the accessible range of 1.6–1.8 eV for the a-Si:H i-layer bandgap is well above the optimum value of ∼1.3–1.4 eV for efficient single junction solar cells, then the highest efficiency Si:H based devices use multijunction configurations. In fact, Si:H thin films have served as the foundation for the first successful multijunction thin film PV technology. The combination of a wider bandgap a-Si:H top cell and a narrower bandgap nc-Si:H bottom cell better utilizes the solar spectrum and, in addition, reduces the impact of light induced degradation in the a-Si:H cell [3–8]. Thus, a common approach for the Si:H multijunction solar cell is the monolithic micromorph tandem, a two terminal device which incorporates top cell a-Si:H with a typical bandgap of ∼1.7 eV and bottom cell nc-Si:H with a bandgap of 1.1 eV. The grain size for nc-Si:H is generally within the range of 50– 500 Å; as a result, the bandgap of this material is close to that of single crystal silicon. Because of the much lower absorption coefficient in the nc-Si:H i-layer, however, a bottom cell nc-Si:H i-layer much thicker (∼2 μm) than the thin top

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cell a-Si:H i-layer (∼0.1 μm) is required for current matching purposes in the a-Si:H/nc-Si:H tandem. When rigid glass plates are used to support the PV devices, then the tandem cell is most often fabricated in the p-i-n sequence and the resulting cell is in the superstrate configuration. In this configuration, the p-layer of the structure is deposited first on the transparent conducting oxide (TCO) coated glass surface. The best such devices yield stabilized cell efficiencies ∼13% [9]. The single-junction and tandem p-i-n solar cell configurations are shown in Fig. 7.1, which provides typical thickness and bandgap values. The dilution of silane gas by hydrogen in the PECVD process, as described by the flow ratio R = [H2]/[SiH4], is key for controlling the microstructure of the Si:H, the volume fractions of a-Si:H and nc-Si:H phases, as well as their depth profiles in the resulting film [4, 10, 11]. As the H2 dilution is increased, the tendency increases for nanocrystal nucleation from the growing amorphous phase or directly from the substrate, and the PECVD growth evolution diagram as deduced by real time spectroscopic ellipsometry (SE) describes this tendency quantitatively. The importance of the diagram lies in the fact that the (a + nc) phase composition and its profile strongly affect the solar cell performance. Detailed real time SE studies have shown that the highest performance a-Si:H solar cells are obtained when the intrinsic Si:H absorber layer is fabricated with the highest possible H2 dilution, but without crossing the a → (a + nc) transition, not only as a function of dilution

Fig. 7.1 Schematic configurations for single-junction a-Si:H and tandem a-Si:H/nc-Si:H solar cells in the p-i-n or superstrate configuration shown on rigid glass. Typical approximate thicknesses are indicated. The solar irradiance enters through the soda lime glass

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ratio R in the early nucleation stage, but also as a function of thickness from the start to the end of the deposition of the device layer [11]. This observation is believed to arise from the beneficial effect of atomic H in the gas phase for passivating unstable defects, breaking weak or strained Si–Si bonds, and terminating the resulting dangling bonds. Real time SE studies have also shown that the highest performance intrinsic nc-Si:H for devices is obtained at the lowest possible dilution level while avoiding transitions across the (a + nc) → a boundary as a function of R and thickness [12]. This observation is believed to arise from the formation of a-Si:H at the grain boundaries under conditions close to the phase boundary of the deposition diagram. The a-Si:H is expected to passivate the grain boundaries effectively, leading to high performance nc-Si:H for devices. Considering the greater complexity of Si:H based multijunction solar cells and their deposition processes compared to single junction cells, SE methods have been found to be especially useful in device characterization [13]. The abilities to characterize the structure of the films and to distinguish the a-Si:H and nc-Si:H phases based on the differences in their optical properties are particularly powerful. In this chapter, applications of two different SE methods for Si:H tandem PV technology are presented. In Sect. 7.2, the application of real time SE will be described for the analysis of the p and i-layer components of the bottom cell nc-Si:H in a-Si:H/nc-Si:H tandem p-i-n solar cells fabricated on TCO coated glass [14, 15]. SE has been applied from the near-infrared to ultraviolet in situ and in real time during Si:H p-i-n tandem cell growth. The Si:H structure and phase composition characterized on the basis of the surface morphology evolution and the complex dielectric function ðε = ε1 − iε2 Þ have been deduced from the analysis of the real time SE data. This structural information has been correlated with PV device performance parameters, including the open circuit voltage VOC, short circuit current density JSC, fill factor FF, and efficiency η. Correlations between the p and i-layer characteristics of the nc-Si:H bottom cell in tandem devices have been identified in this study. Specifically, the effects of plasma power density on the relative a-Si:H and nc-Si:H volume fractions in PECVD p-layers, H2 dilution on the phase evolution of i-layers, and the impacts of these characteristics on PV performance all have been evaluated in Sect. 7.2 of this chapter. In the second component of this chapter presented in Sect. 7.3, both real time and mapping SE are described for the optimization of the n-layer of the a-Si:H p-i-n solar cell used as the top cell of the tandem [15, 16]. In this study, the phase evolution of n-type Si:H has been analyzed in situ by real time SE during the PECVD process. In addition, mapping SE over large areas has been applied as well to study the non-uniformity of the component layers, which can be a limiting factor in Si:H module performance. Analysis of SE mapping data provides information on layer thicknesses, structure, and material optical properties. Correlations between local fundamental properties and dot cell performance parameters have been identified and provide information on the optimization of the cell performance.

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Real Time SE for Process Development: Nanocrystalline Si:H in p-i-n Tandem Solar Cells General Strategy and Approaches

It should be noted that the limitations of ex situ SE in characterizing all the layers of a tandem device motivate the need for real time or in-line measurements of the device structure at various stages in the deposition process. In this section, real time SE results will be presented on a p-i-n tandem cell fabricated from top/bottom cells with a-Si:H/nc-Si:H absorber materials [14, 15]. This is a particularly challenging problem because the bottom cell nc-Si:H exhibits a dielectric function that evolves with thickness, and so requires advanced real time SE modeling. Application of real time SE enables characterization of each layer based on measurements performed during the layer deposition. Although real time SE data sets are technically difficult to analyze, the large quantity of spectra for the sample in a continuous series of thickness states can lead to well defined solutions. Considerable challenges are encountered in the analysis of real time SE data in the actual device structures as described next. The first challenge arises because the starting surface from which growth is initiated is inevitably rough, and as a result, the growth process and the associated real time SE analysis involve two stages. In the first stage, the voids in the surface roughness of the underlying material are filled with the depositing material; simultaneously, surface roughness develops associated with the depositing material [17]. In this first stage, no bulk layer of the depositing material is detectable. In the model for the second stage, a stable (unchanging) roughness layer exists at the interface between the underlying and depositing materials, having been filled in with deposited material in the first stage. Also in the second stage, the bulk layer grows continuously between the interface layer and the surface roughness layer of the depositing material. In the most general models for the two stages of the deposition process, three structural parameters evolve with time during film growth. In the first stage, these include fmi, the content of depositing material within the surface roughness layer of the underlying material; ds, the surface roughness layer thickness for the depositing material; and fvs, the void content in this latter roughness layer. In the second stage, after the interface composition has stabilized, the structural parameters that evolve with time for the depositing material include db, the bulk layer thickness; ds; and fvs. Based on the assumption that the growing film is uniform with thickness, it is best to extract the dielectric function from real time SE data collected after a thickness of bulk layer such that its properties (rather than those of the surface and interface layers) dominate the data. This analysis uses real time SE data collected at M2 different sequential times within the second stage, yielding 2M2N ðψ, ΔÞ values, where N is the number of spectral points [18]. In the analysis, a total of 3M2 + 2N parameters, 3M2 structural values and 2N dielectric function values, must be deduced. Because 3M2 + 2N < 2M2N for any reasonable number of time

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points, then a solution is possible. The critical assumption is that the dielectric function does not depend on thickness. Such a dependence would lead to a dielectric function depth profile that would invalidate the analysis. Different approaches can be used to reduce the number of values that specify the fixed dielectric function in the analysis. The complex dielectric function can be determined, not spectral point by point, but rather as a Kramers-Kronig consistent b-spline with node spacing that depends on the nature of the material (e.g., amorphous, nanocrystalline, or polycrystalline) [19]. Alternatively, the dielectric function can be expressed as a physics-based analytical function [20]. Once the dielectric function is determined from the real time SE data in the second stage, then it can be applied in a straightforward least squares regression analysis of the first stage in which 3M1 structural parameters are obtained, where M1 is the number of time points of the first stage. For high quality amorphous semiconductors, the complex dielectric function of the accumulating film is nearly constant with deposition time and thus uniform with depth throughout the thickness [11]. Small changes in bandgap have been observed in intrinsic a-Si:H absorber layers in solar cells likely due to changes in H-incorporation [21]. For nc-Si:H, however, considerable changes in the dielectric function occur with accumulated film growth, particularly when growth occurs from an amorphous film surface [11, 22]. As a result, a depth profile in the dielectric function is built into the sample, which generates another significant challenge in data analysis. Typically the material in the early stage of growth has the characteristics of the underlying material if it is a-Si:H or mixed phase a-Si:H+nc-Si-H, and the content of nc-Si:H increases with increasing thickness [23]. Such a film growth process is modeled using a different approach based on a virtual interface analysis as described next. In virtual interface analysis, the growing film is modeled as an outerlayer on the surface of a semi-infinite pseudo-substrate that incorporates the past history of the non-uniform deposition [24]. The virtual interface is that between the pseudo-substrate and the outerlayer. On top of the outerlayer, a surface roughness layer is assumed with the dielectric function determined from the Bruggeman effective medium approximation (EMA) as a 50/50 vol% mixture of outerlayer material and void [25]. In this analysis, M pairs of sequential ðψ, ΔÞ spectra are chosen, acquired over a relatively short time period and corresponding to a deposited outerlayer thickness increment on the order of ∼10 Å. During this time period, the dielectric function of the outerlayer and the surface roughness layer thickness can be approximated as constant. From these spectra, the outerlayer deposition rate Ro and the surface roughness layer thickness ds are obtained along with a point-by-point determination of the outerlayer dielectric function. For the first of the M pairs of spectra, the outerlayer thickness is taken to be zero, and for each subsequent pair the outerlayer thickness is do = jRo Δt, where j = 1, 2, . . . , M − 1, and Δt is the time duration between the collection of successive real time SE spectra. The correct pseudo-substrate dielectric function in the analysis is obtained by inversion of the initial ðψ, ΔÞ spectra, which applies a correction for each trial or final value of the surface roughness layer thickness [25]. In the virtual interface analysis, 2N + 2 values are deduced from

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2(M – 1)N data values. Once the first j = 0, 1, 2, . . . , M − 1 set of spectra are analyzed, the analysis moves to the second j = 1, 2, 3, . . . , M set of spectra. The accumulating bulk layer thickness can be determined by integrating the deposition rate. Although virtual interface analysis has its limitations, namely the evolving pseudo-substrate must be optically thick (without interference fringes) [24], it is very effective for tracking the dielectric function of an evolving thin film. As will be seen in Sect. 7.2.3, in the case of nc-Si:H nucleation and growth, the dielectric function obtained in virtual interface analysis can be further analyzed assuming an EMA of a-Si:H, nc-Si:H, and void. This enables determination of the phase evolution of films intended as nc-Si:H during deposition. Another important goal to be achieved is the expression of the complex dielectric function of nc-Si:H using a physics-based analytical model with a small number of free parameters, as has been done for amorphous semiconductors [20, 26]. In many data analysis circumstances, one may seek to introduce a dielectric function with a small number of parameters, rather than determining results spectral point by point. For intrinsic and doped nc-Si:H, the resonance features associated with the band structure critical points are very broad, and further broadening occurs at the elevated temperatures of deposition. As a result, a simple line shape model consisting of a sum of Lorentz oscillators can be used. By using Lorentz oscillators for the three direct gap CPs over the range of 0.75–5.5 eV, one reduces the number of dielectric function parameters by six, since the Lorentz oscillator does not require phase or exponent parameters. The Lorentz oscillator sum associated with the imaginary part of the dielectric function is forced to zero according to an expression consistent with the indirect bandgap of Si [20]. Although in previous descriptions the indirect bandgap parameter was allowed to vary, in this study it is fixed at the known bandgap of c-Si at the deposition temperature based on the assumption that the grain size of nc-Si:H is sufficiently large that quantum effects do not occur. A very general complex dielectric function that covers the case of nc-Si:H is given by ε2 ðEÞ =

No ℏΓ2
D 2  + GðEÞ ∑ Lj ðEÞ ε0 ρ E E 2 + Γ D j=1

ℏΓ A 2 No
D 2 + 2 P 2 + ∑ P ε1 ðEÞ = ε1o − 2 π j=1 E0P − E ε0 ρ E + Γ D where

8  > E − Eg 2 > < E GðEÞ = > > : 0

Z∞ 0

E ′ GðE ′ ÞLj ðE ′ Þ ′ dE , 2 E′ − E2

E > Eg E ≤ Eg

ð7:1Þ

ð7:2Þ

ð7:3Þ

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Lj ðEÞ =

Aj E0j Γj E 2 ðE0j

− E 2 Þ2 + Γ2j E 2

ð7:4Þ

The first term of (7.1) is a Drude component where ρ is the resistivity and ΓD = ℏ ̸ τ, with τ as the Drude free electron scattering time. In the second term, G(E) represents the interband absorption onset shape in ε2 with Eg defining the indirect bandgap. Lj(E) represents the Lorentz line shape function in ε2 for the jth oscillator with an amplitude Aj, a resonance energy E0j, and a broadening parameter Γj [20]. As shown in (7.2), the real part of the dielectric function has four terms, the constant contribution ε1o , the Drude contribution, a contribution from an oscillator with amplitude AP and with resonance energy E0P above the accessible spectral range, and a sum of Kramers-Kronig integrals one for each of the oscillators in ε2 . For nc-Si:H, with Eg fixed at the value for c-Si at the nc-Si:H deposition temperature and with the Drude terms and the term in AP set to zero, then a total of ten parameters are varied in the dielectric function analysis. A goal of this work and continued future research is to reduce the number of variable parameters for intrinsic and doped nc-Si:H [27]. At the minimum, one might expect separate relationships to exist among the three Lorentz oscillator amplitudes, the three resonance energies, and the three broadening parameters. This could lead to a reduction in the number of parameters to four, which would be a significant improvement for analysis of multilayer stacks that include nc-Si:H.

7.2.2

Top Cell Analysis

Top cell characterization by real time SE starts with the analysis of the NSG-Pilkington TEC™ 15 coated glass substrate at the deposition temperature of 200 °C. In addition to a ∼3000 Å thick SnO2-F layer at the top of the TEC™ 15 substrate, ∼200 Å thick layers of undoped SnO2 and SiO2 exist at the interface to the glass, yielding a glass/SnO2/SiO2/SnO2:F structure [28, 29]. Here the focus is on the measurement of the dielectric function of the SnO2:F layer, which is the dominant layer [15]. Figure 7.2 shows experimental ðψ, ΔÞ data collected for the TEC™ 15 substrate just prior to the deposition of the top cell p-layer in accordance with the sequence of Fig. 7.1b. A total of seven structural parameters and eleven dielectric function parameters led to the best fit shown in Fig. 7.2, and the analytical form for the dielectric function of the SnO2:F layer is shown in Fig. 7.3. For this dielectric function, the analytical expression of (7.1)–(7.4) was used with Eg set to zero so that G(E) → 1. The eleven parameters and their confidence limits are included in Table 7.1, including ε1o , the two Drude parameters ðρ, τÞ, as well as (AP, EP), and the six parameters associated with two Lorentz oscillator terms. The deduced structural parameters are shown as the superstrate structure of the completed top cell in Fig. 7.4. Six layer thicknesses are used in the best fit of the TEC™ 15 substrate, including those of the SnO2, SiO2, and SnO2:F films. In fact, the

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Fig. 7.2 Experimental ellipsometric spectra for a TEC™ 15 glass substrate measured in situ at the elevated temperature of 200 °C and at an angle of incidence of 70° (points). The lines represent the best fitting simulation using the dielectric function of Fig. 7.3

Fig. 7.3 Real (ε1) and imaginary (ε2) parts of the SnO2:F dielectric function at the elevated temperature of 200 °C, as simulated using one Drude term, one oscillator with resonance energy well above the upper limit of the spectra, and two Lorentz oscillators. These results were obtained in the fit of Fig. 7.2. The best fitting parameters along with their confidence limits are given in Table 7.1

Table 7.1 Best fitting parameters along with confidence limits that describe the dielectric function of the transparent conducting oxide layer SnO2:F as measured at 200 °C. The dielectric function was simulated assuming one Drude term, two Lorentz oscillators, and one oscillator with resonance energy well above the upper spectral limit (Sellmeier term), the latter yielding no contribution to ε2 . With a lower photon energy limit of 1 eV in this analysis, limitations exist in the ability to extract accurate Drude parameters Dielectric function parameters for NSG Pilkington TEC™ 15 SnO2:F at 200 °C 2.05 ± 0.01 ɛ1o Drude Lorentz 1

Lorentz 2

Sellmeier

Resistivity (Ω cm) Scattering time (fs) A1 (eV) Γ1 (eV) E01 (eV) A2 (eV) Γ2 (eV) E02 (eV) AP [(eV)2] E0P (eV)

(1.02 ± 0.03) × 10−4 22.8 ± 0.6 0.826 ± 0.022 0.658 ± 0.015 4.71 ± 0.01 4.96 ± 0.15 0.487 ± 0.018 5.57 ± 0.01 76.3 ± 2.8 7.64 ± 0.03

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Fig. 7.4 Schematic of a completed a-Si:H p-i-n top cell on a TCO-coated glass substrate (TEC™ 15) along with the fixed and best fit structural parameters including layer thicknesses and component volume fractions. The best fit n-layer structural parameters obtained from the data of Fig. 7.5 are those with confidence limits. The dashed lines show the layers in the SE model, whereas the solid lines separate schematically the different thin film materials

SnO2:F film is modeled with three layer components, a bulk layer 2711 Å thick, a near-surface layer 319 Å thick with a void content of 7 vol%, and a surface roughness layer 260 Å thick with a void content of 49 vol%. In the deposition of the overlying a-Si:H top solar cell on this substrate, the 49 vol% voids in the SnO2:F roughness layer are filled in with p-layer and p/i interface layer materials whose target effective thicknesses are 110 Å and 150 Å, respectively. Real time SE has been applied during the following four depositions of the a-Si:H top cell: the a-Si1−xCx-H p-type window layer, the intrinsic a-Si:H p/i interface layer, and the i and n-layers; as a result, details on the complete structure were obtained as shown in Fig. 7.4. For the p and p/i interface materials, the films were so thin that only the first deposition stage, interface roughness filling, was observed and analyzed. The i and n-layers were thicker, and for those films the second stage, bulk layer growth, was present. The n-layer was modeled as two layers, a-Si:H at the interface to the i-layer and mixed phase Si:H at the top with a deduced nanocrystalline volume fraction of 0.76. The best fit to the real time SE data after

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Fig. 7.5 Ellipsometric spectra of an a-Si:H p-i-n top cell on a TCO coated glass substrate (TEC™ 15) at a 70° angle of incidence (points). The lines represent the best fitting results using the Fig. 7.4 model with four free parameters. This is the top cell structure of an a-Si:H/nc-Si:H tandem

n-layer deposition is shown in Fig. 7.5 and yields the variable parameters with confidence limits in Fig. 7.4. In addition to structural parameters, the critically important i-layer bandgap was determined. The known temperature coefficient of −4.2 × 10−4 eV/°C enables conversion of the 1.610 eV bandgap deduced at the 200 °C deposition temperature to 1.686 eV at 20 °C [30]. The top solar cell model and parameters of Fig. 7.4 as obtained by real time SE summarize the starting point for the studies of the next sub-sections. In these sub-sections, the focus is on the deposition of the p and i-layers of the nc-Si:H bottom solar cell (see Fig. 7.1b) and the challenging real time SE analyses of these two depositions.

7.2.3

Dielectric Functions of Nanocrystalline Si:H n and p-Layers for the Tunnel Junction

For optimization of the critical bottom cell p-layer, a number of depositions were performed on sample structures that simulate the top solar cell structure of Fig. 7.4 [14, 15]. These structures consist of c-Si/SiO2/intrinsic-(a-Si:H)/n-type-(nc-Si:H), as shown in Fig. 7.6, with typical ∼75 Å thick surface roughness on the n-layers. Thus, these n-layers are much smoother than that of Fig. 7.4, which exhibits roughness 150 Å thick. Smoother surfaces result in more accurate dielectric functions and crystalline phase determinations for thin layers in both multi-time and virtual interface analyses. Figure 7.6 shows a schematic of a p-layer deposited on the n-layer of the smoother film stack as obtained by multi-time analysis with the parameters associated with two time points in data analysis, the second point at the end of the deposition when the bulk p-layer thickness is 111 Å. In an evaluation of the crystalline phase evolution, a virtual interface analysis was also performed using real time SE data over the high photon energy range (3–5 eV). This range provides greater surface sensitivity and enables evaluation of the near-surface of the film, beneath the surface roughness layer, in terms of an EMA mixture of a-Si:H, nc-Si:H, and void as shown in Fig. 7.7. Figure 7.8 shows

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Fig. 7.6 Schematic optical model for a nc-Si:H:B p-layer deposited on a thermally oxidized c-Si wafer substrate which was coated in succession with an a-Si:H i-layer and an nc-Si:H:P n-layer. The p-layer structural parameters from two time points are shown

Fig. 7.7 Schematic optical model for Si:H:B p-layers deposited on c-Si/SiO2/i-layer/n-layer structures. A mixture of nc-Si:H, a-Si:H, and voids is assumed for the outerlayer with composition determined from the dielectric function via the EMA, and virtual interface analysis is performed over the high photon energy range of 3–5 eV for surface sensitivity

the virtual interface analysis results, and Fig. 7.9 shows point-by-point representations of the dielectric functions at 200 °C deduced at the PECVD endpoint for p-layers deposited using three radio frequency (rf) power levels. The two higher power depositions show characteristics of a pure nc-Si:H phase at the end of deposition as indicated in Fig. 7.9 whereas the lower power deposition shows the characteristics of high amorphous (55 vol%) and void (11 vol%) contents. These results suggest that a higher plasma power yields a p-layer with continuous development of the crystalline phase, which is desirable in order to nucleate a nc-Si:H i-layer from the p-layer surface.

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Fig. 7.8 Virtual interface analysis results for the time evolution of the mean square error (MSE), the surface roughness layer thickness ds, p, and the nc-Si:H and void volume fractions fb, p-nc, and fb, p-v for p-type Si:H:B depositions on c-Si/SiO2/ i-layer/n-layer structures simulating a top cell. These p-layers were prepared using different rf power densities as shown

The goal of the p-layer optimization is rapid nucleation and well-defined crystalline grain structure which can be evaluated based on the broadening parameter Γ2 = ℏ ̸τ2 of the dominant E2 optical transition observed in Fig. 7.9 as the strong feature near 4.15 eV [31]. The E1 and E1′ transitions appear as weak shoulders on the E2 feature, are more difficult to characterize accurately, and so are less useful for evaluating an excited state relaxation time τ2. The nc-Si:H p-layer dielectric functions of Fig. 7.9 were fit applying the analytical expression of (7.1)–(7.4) with three modified Lorentz oscillators. Table 7.2 summarizes the ten best fit dielectric function parameters for each of the p-layers of Fig. 7.9. A point-by-point representation of the dielectric function typical of the underlying top cell n-layers is also shown in Fig. 7.9. This result was deduced in a virtual interface analysis applied to data acquired during n-layer deposition and is presented for comparison with the p-layers. This n-layer dielectric function has been analyzed similarly, and the associated parameters are also included in Table 7.2. Table 7.2 provides two of the key deposition parameters of the nc-Si:H layers including the H2-dilution flow ratio R = [H2]/[SiH4] and the rf plasma power; all depositions were performed at 200 °C which also is the dielectric function measurement temperature. The parameters for the two fully nc-Si:H

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Fig. 7.9 The dielectric functions measured at 200 °C for p-type Si:H:B layers prepared on c-Si/SiO2/i-layer/ n-layer structures using three different rf power densities as indicated. The solid lines represent best fit analytical expressions for these dielectric functions. Also shown is the analytical form of the dielectric function measured at 200 °C for the R = 100 n-layer used in the analysis of the underlying sample obtained applying virtual interface analysis

p-layers in Table 7.2 are consistent with observations from Fig. 7.9. Specifically, the highest power sample exhibits the smaller values of Γ1 , Γ2 , and Γ3 , indicating larger crystalline grains, and this same sample exhibits continuous crystallite development from initial growth on the n-layer. The parameters for a larger set of dielectric functions for doped nc-Si:H layers prepared on n and i-layer Si:H surfaces under a range of conditions are presented in Figs. 7.10, 7.11, and 7.12. The data set includes p-layers and n-layers for which variations in the hydrogen dilution ratio R = [H2]/[SiH4] are performed. Results of p-layer substrate temperature Tsub series, and two rf plasma power series are included, the latter for the p-layer at substrate temperatures of 120 and 200 °C. The purpose of these scatter plots is two-fold. First, the figures may help to identify layers with the highest crystalline quality based on evaluation of Γ2 . The second purpose is to reduce the number of free parameters in data analysis for thin layers of doped nc-Si:H by linking parameters. Parameter reductions can be expected based on the assumption that the resonance energies En are linear functions of crystallite stress X according to En = Enb + CXn X [32], where Enb represents the associated single crystal Si resonance energy and CXn represents the linear stress coefficient of the energy of the nth oscillator. Eliminating X from the pair of equations for the nth and the n′th oscillator leads to the following linear relationship between En and En′ :

R

250

100

Layer type

p

n

2.841 ± 0.117

192

1.438 ± 0.087

2.480 ± 0.044

128

100

1.343 ± 0.025

ε1o

64

P (mW/cm2) 4.774 89.793 3.549 8.452 63.723 15.126 11.940 49.399 22.978 11.687 65.178 14.968

± ± ± ± ± ± ± ± ± ± ± ±

0.953 1.136 0.504 1.269 2.916 2.009 2.817 7.523 5.713 2.443 5.185 2.912

0.828 1.768 1.121 0.743 1.193 1.716 0.640 0.952 1.545 0.678 1.103 1.493

± ± ± ± ± ± ± ± ± ± ± ±

0.068 0.009 0.101 0.042 0.024 0.100 0.059 0.072 0.145 0.057 0.047 0.129

3.509 4.066 5.140 3.604 4.152 5.060 3.643 4.158 4.916 3.608 4.174 5.115

± ± ± ± ± ± ± ± ± ± ± ±

Parameters of the modified Lorentz oscillator A (eV) Γ (eV) E0 (eV) 0.016 0.008 0.018 0.011 0.004 0.035 0.019 0.009 0.076 0.016 0.007 0.048

1.069

1.069

1.069

1.069

Eg (eV)

Table 7.2 Parameters used in an analytical expression that represents the dielectric functions measured at 200 °C for p-type Si:H:B films prepared on c-Si/ SiO2/i-layer/n-layer structures using different rf plasma power densities. Also included are the parameters in the same analytical expression that describes the dielectric function of the underlying nc-Si:H:P n-layer. The expression is defined by three Lorentz oscillators modified by a common indirect bandgap. A constant contribution to the real part of the dielectric function ε1o is also used as a free parameter

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Fig. 7.10 Resonance energies of the first and third modified Lorentz oscillators that describe the dielectric functions of doped nc-Si:H layers. These results are plotted as functions of the resonance energy of the second oscillator. The solid line is a linear fit to E0,3 and the broken line denotes the average of E0,1. Results for several doped nc-Si:H samples are shown

Fig. 7.11 Broadening parameters of the first and third modified Lorentz oscillators that describe the dielectric functions for several doped nc-Si:H layers. These results are plotted as functions of the broadening parameter of the second oscillator



 CXn CXn En = Enb − En′ b + E ′. CXn′ CXn′ n

ð7:5Þ

Figure 7.10 shows E0,1 and E0,3 in correlation with E0,2. Associating the E0,2 oscillator energy with the nearest crystalline Si critical point (CP), that of E2(X) located at 4.22 eV for a temperature of 200 °C [33], an increase in E0,2 over the range of 4.12–4.20 eV would be associated with a reduction in stress. At the same time, the best fit linear correlations in E0,3, corresponding to the E1′ CP lead to variations over the range 4.8–5.2 eV which bring these resonance energies closer to

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Fig. 7.12 The constant offset ɛ1o and the amplitude parameters of the modified Lorentz oscillators that describe the dielectric functions of several doped nc-Si:H layers. These results are plotted as functions of the relative void volume fraction, which was obtained by using the dielectric function of the densest film of the p-layer H2dilution series with R = 225 and that of void in the Bruggeman EMA to simulate the dielectric functions of all other nc-Si:H materials. The solid lines are linear fits and the horizontal broken lines denote average values

the single crystal E1′ critical point at 5.19 eV for the substrate temperature of 200 °C [33]. All E0,1 values are considerably higher than the associated crystalline Si E1 CP of 3.29 eV; however, the variation is weak ∼0.1 eV compared to the average ∼0.3 eV difference from the c-Si value. The higher energy may occur if the excitonic transition associated with this lowest energy direct CP is affected by crystallite size, leading to a widening of the associated bandgap. Thus, one can conclude E0,3 can be linked to E0,2 through the expression in Fig. 7.10, E0,3 = 2.37 E0,2 − 4.74 eV, and E0,1 can be fixed at its average value of 3.605 eV. This can reduce the number of variable parameters in the dielectric function expression from ten to eight. A similar analysis can be performed on the broadening parameters, correlating the parameters of the first and third oscillators with that of the second one, the strongest oscillator. Applying the assumption that each oscillator broadening parameter is controlled by the same grain boundary scattering mechanism, then the following linear relationships are expected   Vgn Vgn Γn = Γnb − Γn′ b + Γn′ Vgn′ Vgn′

ð7:6Þ

between the nth and the n′th parameters [31]. Here Γnb and Γn′ b represent the associated single crystal Si broadening parameters (0.16, 0.11, 0.18 eV at 200 °C for n = 1, 2, 3, respectively [33]) and Vgn and Vgn′ represent group velocities of

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excited carriers that undergo scattering for the nth and the n′th oscillators. The data points for Γ1 in Fig. 7.11 have been fit assuming a linear relationship with the result being Γ1 = 0.463Γ2 + 0.193 eV, which demonstrates behavior consistent with (7.6). The correlation for Γ3 is unclear since the third resonance is very weak. It is reasonable to fix this third oscillator’s broadening parameter at the average Γ3 = 1.514 eV for all samples. By further applying these two results for Γ1 ðΓ2 Þ and Γ3 , one can reduce the number of free parameters in the modified Lorentz oscillator expression from eight to six. The parameters ε1o and all three oscillator amplitudes have been correlated to the relative void volume fractions obtained by EMA fits of the dielectric functions. The reference material of lowest void fraction was found to be a p-layer fabricated at R = 225 with a substrate temperature of Tsub = 120 °C and a plasma power of P = 128 mW/cm2. This p-layer exhibited the highest amplitudes of the complex dielectric function over the measured range. Thus, the nc-Si:H dielectric function of this p-layer and that of void were then applied in the EMA to model all other dielectric functions in order to obtain their relative void fractions. With this approach, the least dense film is that prepared at the lowest H2 dilution of R = 80, an n-layer deposition. It is noted in Fig. 7.12 that ε1o and the dominant amplitude A2 show expected linearly decreasing trends as the relative void volume fraction increases whereas the much weaker A1 and A3 values show no systematic trends. In the parameterization, the results in Fig. 7.12 suggest that it is possible to fix A1 and A3 at their average values of 14.41 and 14.55 eV and to link A2 to the void fraction fv through the expression of the form A2 = −150.0 fv + 72.8 eV. Because of the large scatter in ε1o , and its ability to accurately control the overall amplitude of ε1 , it is likely that this parameter is needed in addition to fv. Thus, in summary, by applying the relations in Figs. 7.10, 7.11, and 7.12 as recommended here, one can reduce the number of parameters that define the dielectric functions of doped nc-Si:H materials from ten to four, including fv, ε1o , E2, and Γ2 . The parameters are expected to provide information on the relative density via the void fraction ðfv , ε1o Þ and measures of stress (E2) and grain size ðΓ2 Þ. One should be concerned with the variations in measurement temperature for the nc-Si:H samples in Figs. 7.10, 7.11, and 7.12. Most samples in these figures were measured in the temperature range from 120 to 200 °C. For single crystal Si, this range leads to variations of (±0.016, ±0.011, ±0.030) eV for the E0,1, E0,2, and E0,3 transition energies and (±0.008, ±0.005, ±0.011) eV, for the Γ1 , Γ2 , and Γ3 broadening parameters, respectively [33]. Thus, the effect of the temperature range is within the confidence limits, although improved statistics may be possible by adjusting all data to the same temperature using the temperature coefficients given elsewhere for p-type nc-Si:H [20]. It should be emphasized that the parameterization in these figures is most relevant for the temperature of ∼150 °C, with a possible range of applicability of ±50 °C; thus for a room temperature dielectric function parameterization adjustments are required according to the available temperature coefficients. The dielectric functions generated using the oscillator parameters in Table 7.2 obtained for the smoother sample structure have been applied to fit the experimental

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data over the spectral range from 1 to 5 eV for bottom cell Si:H:B p-layers on the complete (TEC™ 15)/p-i-n a-Si:H top solar cell structures. In this analysis, the structural parameters of the bottom cell Si:H:B p-layers can be obtained. Figures 7.13 and 7.14 show the optical model and ellipsometric spectra measured at 200 °C at the end of deposition for the sample incorporating the nc-Si:H:B p-layer deposited with P = 128 mW/cm2 on the (TEC™ 15)/p-i-n top cell structure. The final p-layer structural parameters as well as the effective thickness and MSE for each of the three film structures are given in Table 7.3, as determined using the optical model shown in Fig. 7.13.

Fig. 7.13 Schematic optical model for a bottom cell Si:H:B p-layer deposited on a structure consisting of a (TEC™ 15)/p-i-n a-Si:H top solar cell. This structure describes the P = 128 mW/ cm2 deposition in the center column of Table 7.3. The dashed lines show the layers in the SE model, whereas the solid lines schematically demarcate the individually-deposited films

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Fig. 7.14 Ellipsometric spectra at a 70° angle of incidence for a nc-Si:H:B p-layer deposited on a structure consisting of a (TEC™ 15)/p-i-n a-Si:H top solar cell (points). The lines represent the best fitting results using the three-parameter model shown in Fig. 7.13

Table 7.3 Best fitting structural parameters at the end of deposition along with their confidence limits for Si:H:B p-layers deposited on structures consisting of (TEC™ 15)/p-i-n a-Si:H top solar cells. The rf plasma power and deposition time are provided for each p-layer Structural parameters of bottom cell p-layer in a-Si:H/nc-Si:H tandem P (mW/cm2) Time (s) MSE Surface roughness thickness, ds,p2 (Å) p-layer volume fraction in surface roughness, fs,p2 p-layer bulk thickness, db,p2 (Å) n/p interface thickness, di5,n (Å) p-layer volume fraction in n/p interface, fi5,p2 p-layer effective thickness (Å)

7.2.4

64 1000 17.06 130.0 ± 0.9 0.512 ± 0.003

128 600 18.75 144.5 ± 0.7 0.451 ± 0.003

192 550 17.61 137.5 ± 0.7 0.417 ± 0.004

76.5 ± 1.3 129.0 0.500 207.6

56.4 ± 1.0 150.2 0.500 196.6

44.3 ± 0.8 173.6 0.500 188.4

Dielectric Functions of Bottom Cell Nanocrystalline Si:H i-Layers

In this sub-section, detailed presentation and discussion of the bottom cell nc-Si:H i-layer dielectric functions are given [14, 15]. The underlying nc-Si:H p-layer in these studies was fabricated using the intermediate power level of P = 128 mW/cm2. The only i-layer variable is the hydrogen dilution ratio R = [H2]/[SiH4], which is set at a value within the range from 2 to 40. The i-layer PECVD parameters that were held constant include a substrate temperature of 200 °C and a power density of 128 mW/cm2. The plasma excitation frequency for the bottom cell i-layer was set in the very high frequency (vhf) range at 60 MHz. The higher excitation frequency promotes the formation of nanocrystallites relative to the value of 13.56 MHz used for the standard rf PECVD of the top cell and doped layers [2]. A point-by-point dielectric function for each of the bottom cell i-layers prepared with R = 2–40 on the nc-Si:H p-layer material was determined by applying

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multi-time analysis to three sets of SE data acquired near the end of each deposition. The dielectric function of the nc-Si:H i-layer for each R value is assumed to have stabilized without any thickness dependence, that is, after a thick nc-Si:H i-layer has evolved. Figure 7.15 shows the best fit analytical expressions to these dielectric functions assuming three Lorentz oscillators modified by the indirect bandgap of Si of 1.069 eV at the deposition and measurement temperatures of 200 °C. The best fit parameters of the analytical expressions are shown in Table 7.4. It is evident that all five dielectric functions for i-layers prepared with R = 2–40 closely overlap and that the dielectric function amplitudes for the i-layers are much lower than those of the doped layers of Fig. 7.9. This may be caused by the large i-layer bulk and surface roughness layer thicknesses, with the possibility of surface connected microvoids, as well as voids propagating from the p-layer surface roughness. Figure 7.16 presents the values of the parameters listed in Table 7.4 in plots as functions of R. The E0,2 and E0,3 resonance energies in Fig. 7.16 start at low R near the single crystal values of 4.22 eV and 5.19 eV at 200 °C, respectively. E0,2 decreases to a minimum near R = 20, and increase again for the R = 40 value. This behavior suggests that film stress increases with R up to R = 20, and then decreases. A similar trend is observed for E0,3, however, the confidence limits become very large at high R. The E0,1 resonance energy shows behavior similar to that of the p and n-layers in Sect. 7.2.3. Although the E0,1 energies for the i-layers, 3.48–3.50 eV, are much larger than the single crystal value of 3.29 eV at 200 °C,

Fig. 7.15 The dielectric functions at 200 °C for bottom cell nc-Si:H i-layers, as determined by multi-sample analysis. The i-layers were prepared using different hydrogen dilution ratios (R = 2, 5, 10, 20, and 40) within a chamber dedicated to vhf-PECVD of the i-layers [14]

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Table 7.4 Parameters used in an expression that represents the dielectric functions measured at 200 °C for nanocrystalline Si:H i-layers prepared using different hydrogen dilution ratios for the bottom cell. The expression is defined by three Lorentz oscillators modified by a common indirect bandgap. A constant contribution ε1o to the real part of the dielectric function is also used as a free parameter Bottom cell nc-Si:H i-layer at 200 °C Modified Lorentz oscillator R ε1o A (eV) Γ (eV) 2

0.854 ± 0.066

5

0.687 ± 0.076

10

0.758 ± 0.072

20

0.287 ± 0.116

40

0.328 ± 0.104

4.425 48.008 17.113 4.983 42.155 24.025 5.266 43.262 22.494 8.943 39.298 26.562 6.369 40.537 27.466

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.578 2.109 1.949 0.654 2.999 3.075 0.638 2.786 2.813 1.469 6.964 7.525 0.948 5.004 5.390

0.562 1.236 1.837 0.584 1.166 2.310 0.586 1.166 2.278 0.705 1.129 3.096 0.618 1.145 2.669

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

E0 (eV) 0.039 0.031 0.113 0.041 0.034 0.148 0.038 0.032 0.142 0.066 0.050 0.463 0.052 0.045 0.263

3.500 4.199 5.253 3.498 4.177 5.152 3.494 4.170 5.152 3.486 4.136 5.077 3.494 4.169 5.112

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

Eg (eV) 0.007 0.004 0.030 0.007 0.004 0.058 0.007 0.004 0.055 0.009 0.005 0.216 0.008 0.005 0.119

1.069

1.069

1.069

1.069

1.069

this range is lower than the average value of 3.62 eV for the doped layers. This behavior would be expected for a larger grain size or a lower crystallite defect density in the i-layers compared to the doped layers. Considering next the broadening parameters in Fig. 7.16, it is noted that the broadening parameter Γ2 of the dominant oscillator E0,2 tends to decrease with increasing R for R < 20. This is an expected trend that could be attributed to an increase in grain size or an improvement in crystallite quality with increasing R to R = 20. In contrast, Γ1 and Γ3 show the opposite behavior, namely increases with increasing R over this range. This apparent inconsistency may be attributable to dielectric function inaccuracies since the E0,1 and E0,3 oscillators are relatively weak shoulders on the dominant E0,2 oscillator. The similar overall amplitudes of the analytical forms of the dielectric functions for the bottom cell i-layers in Fig. 7.15 suggest similar void volume fractions for all i-layer films. In spite of this, different trends are observed versus R in the constant contribution ε1o and the oscillator amplitudes. Such variations are likely to be due to correlations, since the weaker A1 and A3 amplitudes increase as the dominant ε1o and A2 amplitudes decrease with R, at least for the lower R values. Because of the inconsistent trends observed in Fig. 7.16, likely caused by correlations, it seems reasonable to attempt a reduction in the number of free parameters in modeling the dielectric functions of the nc-Si:H i-layers, as was done in Sect. 7.2.3 for the doped nc-Si:H. The goal is to identify relationships or constants

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Fig. 7.16 Dielectric function parameters for bottom cell nc-Si:H i-layers measured at 200 °C and plotted versus the hydrogen dilution ratio, assuming an analytical form given by three modified Lorentz oscillators and an energy-independent contribution to ε1 . The broken lines are visual guides to the data

that may be employed for this purpose, starting with the resonance energies in Fig. 7.17. The panel for the correlation of E0,3 with E0,2 includes the critical point energies for single crystal silicon [33]. This correlation suggests that for the i-layers E0,3 can be linked to E0,2 in a parameterization according to E0,3 = 3.71 E0,2 − 10.3 eV such that the variations in these energies are caused by stress, as was suggested for the doped nc-Si:H. In fact, this trend is close to that observed for the larger set of doped nc-Si:H and roughly consistent with the single crystal data point in Fig. 7.17, which would correspond to zero stress. In contrast, the variations in E0,1 are much smaller, and its range of values is not understandable in terms of stressed crystallites. As a result of the smaller variations, E0,1 can be fixed at its

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Fig. 7.17 Resonance energies of the first and third Tauc-Lorentz oscillators that describe the dielectric functions of the bottom cell nc-Si:H i-layers at 200 °C. These results are plotted as functions of the resonance energy of the second oscillator. The solid lines are the linear fits to the i-layer results with the equations given in each panel, and the horizontal dashed line represents the average value of E0,1. The circular point in the lower panel identifies the values of E0,2 and E0,3 for single c-Si. The dotted line is the linear fit of the i-layer results, constraining the fit to pass through the point for single c-Si. The average value of E0,1 and the linear fit to E0,3 for the doped layers from Fig. 7.10 are given by the dot-dashed lines

average value of E0,1 = 3.494 eV for this series, which is considerably lower than the range of values for doped nc-Si:H, as shown in Fig. 7.17. The broadening parameters of the first and third resonances are plotted as a function of the broadening of the dominant E0,2 oscillator in Fig. 7.18. Because the same mechanism that leads to variations in broadening of the E0,2 oscillator is not observed for the other two oscillators, the simplest consistent method for parameter reduction is to fix the broadening parameters of the two weaker oscillators to their average values, given by Γ1 = 0.611 eV and Γ3 = 2.438 eV. Differences may arise between the behavior observed for doped and i-layers since the i-layers have higher void fractions whereas the doped layers have higher densities of scattering centers due to defects, including the respective dopant atoms themselves. The correlation plot of the nc-Si:H i-layer dielectric function amplitudes including the constant ε1 offset versus the relative void fraction is given in Fig. 7.19 which uses the R = 225 p-layer as a reference. Due to the similarity of void fractions for all i-layers, there is no clear correlation among the i-layer samples in this plot. In order to obtain correlations among the i-layer samples similar to those for the doped layers, dielectric function measurements for i-layers prepared with different thicknesses or under different conditions are required. Comparing the results for the i-layers with the trends observed for the doped layers, the average value of A2 is roughly consistent with the trend observed for the doped layers

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Fig. 7.18 Broadening parameters of the first and third Tauc-Lorentz oscillators that describe the dielectric functions of the bottom cell nc-Si:H i-layers at 200 °C. These results are plotted as functions of the broadening parameter of the second oscillator. The solid lines are the linear fits to the i-layer results with the equations given in each panel. The horizontal broken lines represent the average values of Γ1 and Γ3 for the i-layers. The dot-dashed lines describe the linear fit of Γ1 and the average value of Γ3 for doped layers from Fig. 7.11

Fig. 7.19 The constant offset ɛ1o and the amplitude parameters of the modified Lorentz oscillators that describe the dielectric functions of nc-Si:H i-layers at 200 °C. These results are plotted as functions of the relative void volume fraction, which was obtained by using the dielectric function of the densest film of the p-layer H2dilution series and that of void in the EMA to simulate the dielectric functions of all other nc-Si:H materials. The horizontal broken lines represent the average values from the i-layer series, and the dot-dashed lines represent either averages for A1 and A3 or linear trends for ε1o and A2 from the doped layer series of Fig. 7.12

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whereas the average value of ε1o for the i-layers is lower than the corresponding doped layer trend. Thus, a possible strategy for parameter reduction for these i-layers is to use (i) fixed average values for A1 and A3, (ii) the trend from A2 given by the doped layers specified by the free parameter fv, and a variable value of ε1o . This approach would be consistent with that developed for nc-Si:H doped layers.

7.2.5

Real Time SE and Growth Evolution Diagram of nc-Si:H i-Layer Evolution

In the analysis of the real time SE data for the nc-Si:H i-layer of the bottom cell, plots of the bulk layer thickness versus time can be obtained by applying each of the five analytical expressions of Table 7.4 for the dielectric functions [14]. From the bulk layer thickness versus time, the deposition rate Rd can be obtained as an average over the deposition time from beginning to end. Figure 7.20 depicts Rd as a function of the H2-dilution ratio R. The deposition rate Rd decreases rapidly as R increases over the range of R = 2–20 and stabilizes for R ≥ 20. In order to characterize the microstructural and phase evolution of each bottom cell i-layer, the model shown in Fig. 7.7 was applied to analyze the real time SE data over the spectral range from 3 to 5 eV. This model includes an outerlayer along with a surface roughness layer, whereby the former was simulated using a three component EMA of a-Si:H, nc-Si:H, and void. The dielectric function of a-Si:H used in the EMA of the semi-infinite medium is given as an analytical expression consisting of a single Cody-Lorentz oscillator with fixed Eg = 1.68 eV and with all other parameters linked to the bandgap with relationships adjusted for the 200 °C temperature. The resulting MSE, surface roughness layer thickness ds,i 2, and nc-Si:H and relative void volume fractions fb,i 2-nc, and fb,i 2-v are plotted versus bulk layer thickness db,i 2 in Fig. 7.21. Considering next Fig. 7.21, a surface smoothening effect is observed in the initial stage of each nc-Si:H i-layer deposition. Such a smoothening effect is more

Fig. 7.20 Deposition rate Rd versus hydrogen dilution ratio R = [H2]/[SiH4] for bottom cell Si:H i-layers prepared using vhf-PECVD at 60 MHz with different H2-dilution ratios of R = 2, 5, 10, 20, and 40 (points). The line is a visual guide

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Fig. 7.21 Mean square error (MSE), surface roughness layer thickness (ds,i 2), and bulk layer nanocrystalline and relative void volume fractions (fb,i 2-nc and fb,i 2-v, respectively), plotted versus bulk layer thickness for Si:H i-layers prepared on Si:H p-layers in the tandem solar cell configuration. These i-layers were fabricated by vhf-PECVD at 60 MHz with different hydrogen dilution ratios of R = 2, 5, 10, 20, and 40

pronounced for the i-layers prepared at lower hydrogen dilution ratio. This effect is consistent with the renucleation of smaller nanocrystallites from the p-layer that smoothen the growing film surface. Other key features in this figure that support this interpretation include an observed subsequent roughening transition, a maximum in the surface roughness layer thickness, and a second more abrupt decrease in surface roughness. This later stage growth behavior indicates that the i-layers undergo a phase transition from a mixed phase which is deposited in the earlier stage of i-layer deposition to a coalescing nanocrystalline phase [(a-Si:H + nc-Si:H) → nc-Si:H] at the roughness maximum. A renucleation process and subsequent small grain growth may arise from a transient effect in the initial striking of the plasma that disrupts continued evolution of the nanocrystallites from the p-layer surface to the p/i interface region. This transient effect could be a gas phase compositional change with time or interface disruption that generates a damaged region. Over time, however, as the plasma stabilizes and the p/i interface is buried, the nucleating nanocrystals increase in size as indicated by the subsequent roughening effect.

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Figure 7.22a shows a growth evolution diagram that depicts the bulk layer thickness at which the nc-Si:H volume fraction assumes specific values in plots as a function of the H2-dilution ratio R used in the deposition process [11]. The uppermost line with fb,i 2-nc = 1 represents the bulk layer thickness at which the transition occurs from mixed-phase Si:H (a-Si:H + nc-Si:H) to stable phase nc-Si:H. The diagram shows typical behavior in that the transition shifts to decreasing bulk layer thickness with increasing R; the most rapid shift occurs between R = 10 and R = 20. Extensive studies have demonstrated that under specific ranges of deposition conditions, including high H2 dilution ratio for example, Si:H films first nucleate as a-Si:H or mixed-phase materials and then evolve into inverted cone-like nanocrystalline structures as growth proceeds [11]. The nucleation density Nd and cone half angle θ of the nucleating nanocrystallites can be estimated from real time SE results using the difference between the bulk layer thicknesses (Δdb) at which the coalescence and nucleation of nanocrystalline inclusions occur, as well as the associated difference in the surface roughness thickness ðΔds Þ. The nucleation is identified by an abrupt increase in roughness as crystallites grow preferentially relative to the surrounding material. Coalescence is identified by a clear maximum

Fig. 7.22 a Growth evolution diagram plotted as a function of the H2-dilution ratio for 60 MHz vhf-PECVD of bottom cell Si:H deposited on a Si:H p-layer in the tandem configuration (points). Depicted are the (mixed-phase)-to-(stable nanocrystalline phase) Si:H transition (diamonds) and the bulk layer thickness contours at which the nc-Si:H volume fraction is constant. b Nucleation density plotted as a function of R for the bottom cell Si:H i-layers (points). The lines in (a) and (b) are visual guides

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in the surface roughness layer thickness. The following equations describe the nucleation geometry θ = cos − 1 Nd =



 Δdb , Δdb + Δds 1

KðΔdb Þ2 tan2 θ

,

ð7:7Þ ð7:8Þ

where K is a constant defined by the surface area fraction occupied by the bases of the nanocrystalline cones at the onset of coalescence [23]. The value of K depends on the initial distribution of the crystalline nuclei. In this study, it is assumed that the crystalline nuclei lie on a square lattice and, thus K = 4. Figure 7.22b shows the nucleation density determined from (7.7) and (7.8) plotted as a function of R as deduced from the data in Fig. 7.21. The nucleation density is observed to increase rapidly with increasing R with the largest step between R = 10 and R = 20.

7.2.6

Process-Performance Correlations for a-Si:H/nc-Si:H Tandem Solar Cells

Table 7.5 provides the deposition conditions of the individual layers of the a-Si:H/ nc-Si:H tandem solar cells, where ‘V’ indicates the parameters that have been varied in studies of process-performance correlations [14]. One goal of this set of depositions was to explore the role of enhanced crystallinity in the bottom cell p-layer on the crystalline development in the overlying i-layer. A second goal is to explore the effects of elevated total gas pressure of 1.5 Torr on the formation of the recombination junction, the bottom cell i-layer, and the resulting performance of the solar cell. Figure 7.23 shows the device performance results for tandem cells that were fabricated under identical conditions, with the exception of the bottom cell Si:H:B p-layers. These p-layers were prepared at the three different rf power levels of P = 64, 128, and 192 mW/cm2 with final film structures given in Table 7.3. The H2-dilution ratio for the bottom cell i-layer of these solar cell depositions was fixed at R = 20; all other deposition details are given in Table 7.5. The VOC values of the set of cells fabricated with the lowest power p-layer are significantly higher and the short circuit current density values (JSC) are significantly lower compared to those for the sets of cells with p-layers fabricated using the two higher plasma power levels. The high VOC of the set of tandem cells with the bottom cell p-layer fabricated at low plasma power is caused by the properties of the p/i interface and its influence on subsequent i-layer deposition [11]. In particular, the evolution of the i-layer is expected to be controlled by the structure of the low plasma power p-layer with its higher a-Si:H volume fraction, resulting in the higher VOC. It is clear that

Tsub (°C)

200 200 200 200 200 200 200 RT

Layer

p p/i i n p i n Ag

400 1000 450 1500 1500 1500 350 5

ptotal (mTorr)

13.56 13.56 13.56 13.56 13.56 60 13.56 13.56

Plasma f (MHz) 9.5 13 13 32 V 128 9.5 920

P (mW/ cm2) – – – 0.5 – – 0.5 –

1 – – – 0.5 – – –

– – – – – – – 10 13 6 20 2 2 5 10 –

5% PH3 in H2

Gas flow (sccm) Ar SiH4 5% B2H6 in H2 8 – – – – – – –

CH4

– 360 10 200 500 V – –

H2

50 800 800 1000 V V 120 1800

Time (s)

110 150 1500 250 1500 20,000 250 20,000

Target thickness (Å)

Table 7.5 Deposition conditions for the component layers of the a-Si:H/nc-Si:H tandem solar cells fabricated in this investigation. The power density for the p-layer of the bottom cell and the hydrogen gas flow for the i-layer of this cell are variables in this study, as denoted “V”

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Fig. 7.23 Performance parameters of open circuit voltage (VOC), short circuit current density (JSC), fill factor (FF), and efficiency for Si:H tandem solar cells incorporating bottom cell Si:H:B p-layers prepared with different rf power density levels of P = 64, 128, and 192 mW/cm2. The i-layer of the bottom cell used in this p-layer comparison was prepared using a hydrogen dilution ratio of R = 20

the range and maximum VOC of this set of cells, the latter being VOC ∼ 1.7 V, is characteristic of a tandem device with two a-Si:H cells, with the top and bottom cells generating voltages of ∼0.8–0.9 V. The low JSC is also likely to reflect the initial amorphous phase within the i-layer of the bottom cell, which is not collecting sufficient current due to its inhomogeneous structure, evolving from a-Si:H to nc-Si:H. The low current generated by the bottom cell then limits current through the entire device. For the p-layer prepared at the lowest plasma power, the amorphous region of the bottom cell i-layer adjacent to the p/i interface results from the amorphous phase of the underlying p-layer. Specifically, the p-layer suppresses the growth of nanocrystallites in the i-layer under the relatively low R = 20 H2-dilution conditions, promoting instead the growth of the amorphous phase. The amorphous region of the bottom cell i-layer exerts a dominating effect on the overall tandem cell performance. A weaker effect may be related to the nature of the n/p interface formed under the low power p-layer conditions. Under these conditions, the interface may not serve as an effective recombination junction for the tandem solar cell. In fact, a higher density of defects may be needed at this interface. In contrast, the device performance for the sets of cells having p-layers prepared at P = 128 and 192 mW/cm2 are similar to one another, an observation that is consistent with the similarity in the dielectric functions of the p-layers as shown in Fig. 7.9. For these two similar sets of cells, the VOC values are consistent with an a-Si:H/nc-Si:H

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tandem solar cell (as opposed to an a-Si:H/a-Si:H tandem). In fact, the observed maximum VOC value of ∼1.25 V from the two sets of cells is consistent with an a-Si:H top cell generating a voltage of ∼0.85 V and a bottom cell generating a maximum voltage of ∼0.4 V. Figure 7.24 summarizes the device performance of two series of tandem solar cells that incorporate bottom cell nc-Si:H p-layers prepared at rf power levels of 128 and 192 mW/cm2. On each of these two types of p-layers, a series of Si:H bottom cell i-layers was deposited using the H2 dilution ratio R as a variable deposition parameter. Five and three different hydrogen dilution ratios of R = 2, 5, 10, 20, and 40, and R = 10, 20, and 40 were applied in i-layer depositions on the nc-Si:H p-layers prepared at rf power levels of 128 and 192 mW/cm2, respectively. Considering the full set of data including cells with both p-layers, it is clear that the average open circuit voltage VOC decreases with increasing hydrogen dilution ratio R. This may indicate a change in the bottom cell p/i interface region from a dominant

Fig. 7.24 Performance parameters of open circuit voltage (VOC), short circuit current (JSC), fill factor (FF), and efficiency for Si:H tandem solar cells incorporating bottom cell i-layers prepared with different hydrogen dilution ratios R enumerated along the abscissa. The bottom cell nc-Si:H p-layers used in this i-layer comparison were prepared at rf power density levels of P = 128 mW/cm2 (black open symbols) and 192 mW/cm2 (shaded symbols)

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amorphous phase contribution to a nanocrystalline phase contribution with increasing R. In addition at low R, there is a much broader distribution of VOC values, demonstrating that under these conditions there is a much stronger spatial dependence of the bottom cell i-layer structure adjacent to the p/i interface region. In contrast to VOC, the average short circuit current JSC increases as the H2-dilution ratio R increases for R values from R = 2–20, yielding a maximum JSC at R = 20. The maximum fill factor is highest at the lowest R value and decreases as R increases to R = 10. Abrupt increases in the maximum and average fill factors are observed between R = 10 and 20, with the maximum values nearly reaching the overall maximum possible with R = 2. The fill factor distribution tends to narrow with increasing R to R = 20, reaching a much narrower width for the two high H2-dilution ratios of R = 20 and 40. This behavior again reflects a stronger spatial non-uniformity of the bottom cell structure at the lowest R values. From the device performance shown in Fig. 7.24, the tandem solar cells separate into two groups irrespective of the rf power used in the deposition of the bottom cell p-layer. The first group includes R = 2, 5, and 10, whereas the second group includes R = 20 and 40. The transition between the two groups occurs in the same range of R as the large changes in the evolution of surface roughness and nanocrystalline fraction as determined by the real time SE data analysis shown in Fig. 7.21, the growth evolution diagram in Fig. 7.22a, and the nucleation density in Fig. 7.22b. This change is characterized by abrupt reductions in (i) the thickness at which the roughening transition occurs associated with the renucleation of crystallites starting from mixed-phase Si:H and (ii) the thickness at which the coalescence transition occurs from mixed-phase to stable-phase nc-Si:H. The first transition decreases from 2500 to 400 Å in the i-layer bulk thickness as R increases from R = 10 to 20, and the second transition decreases from ∼6000 to 1000 Å in the i-layer bulk thickness as R increases from R = 10–20. As a result, for the low R group of cells, the volume fraction of nc-Si:H in the i-layer remains below 0.65 for at least the first 3000 Å of growth. Clearly, the maximum open circuit voltages VOC of the first group are much higher compared to those of the second group, and the average VOC for this first group is decreasing with increasing R. In fact, between the first and second groups, i.e., between R = 10 and 20, the average and maximum VOC show a step decrease with the increase in R. In contrast, the average and maximum fill factor FF and to a lesser extent short circuit current JSC exhibit step increases between R = 10 and 20. Overall, the trends in JSC and FF dominate, and the average and maximum efficiency of the first group are lower than those of the second group. Both average device performance and real time SE data analysis results indicate that the p/i interface of the first group has a large spread of characteristics, whereas that of the second group is dominated by the nanocrystalline phase. The large spread in VOC for the first group indicates that depending on the location on the 15 cm × 15 cm sample, some cells are dominated by the amorphous phase with VOC as high as 1.7 V whereas others are dominated by the nanocrystalline phase with VOC as low as 1.25 V. As noted earlier, this behavior is a result of spatial non-uniformity that occurs under the deposition conditions used for the low R films.

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In the following paragraphs, the further implications of the above observations will be discussed. The open circuit voltage VOC sensitively reflects the properties of the p/i interface region, in particular the phase composition and bandgap of the i-layer adjacent to the p/i interface [11]. Typically for mixed phase i-layer materials, the open circuit voltage VOC increases as the volume fraction of amorphous phase in the i-layer at the interface increases and, for single phase i-layer materials, as the bandgap of the phase increases. To explore these effects, the device performance parameters of JSC, FF, and efficiency, also including the series and shunt resistances Rs, and Rshunt, respectively, are plotted versus the open circuit voltage VOC in Fig. 7.25 for all solar cell depositions. The motivation for presenting these plots is to evaluate the effect of the nature of the bottom cell p/i interface region on the performance parameters of the device. It can be observed in Fig. 7.25 that the short circuit current JSC tends to decrease continuously with increasing open circuit voltage VOC. One possible reason for this behavior is the increase in the effective thickness of the amorphous component in the i-layer adjacent to the p/i interface as VOC increases. This in turn leads to

Fig. 7.25 Performance parameters of short circuit current (JSC), fill factor (FF), efficiency, as well as series resistance (Rs), and shunt resistance (Rshunt) plotted versus the open circuit voltage (VOC) for Si:H tandem solar cells incorporating bottom cell i-layers prepared with different hydrogen dilution ratios R. The bottom cell nc-Si:H p-layers used in this i-layer comparison were prepared at two different rf power density levels of P = 128 mW/cm2 (solid symbols) and 192 mW/cm2 (open symbols)

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reduced absorption by the bottom cell since the bandgap of a-Si:H is wider than that of the desired nc-Si:H phase. The net effect is a reduction in current generated by the bottom cell and a mismatch in current generated by the two cells. The current output of the tandem device is then limited by the reduced bottom cell current. The fill factor, on the other hand, initially decreases gradually as the open circuit voltage VOC increases above 1.2 V; however, a more rapid increase in fill factor occurs when the open circuit voltage VOC increases above 1.6 V. This behavior suggests that when the i-layer region adjacent to the p/i interface is predominantly nanocrystalline Si:H with VOC being controlled by this phase, the fill-factor is relatively high. The limitation on the fill factor under these conditions is a low apparent shunt resistance in fact associated with voltage-dependent collection, characteristic of a low quality nanocrystalline bottom cell i-layer. A relatively high fill factor is also obtained when the i-layer region adjacent to the p/i interface is predominantly a-Si:H with VOC being controlled by this phase such that the cell behaves as an a-Si:H same bandgap tandem cell. The limitation in this case is a high series resistance. At intermediate VOC values the fill-factor is reduced when the intrinsic Si:H material transitions between amorphous and nanocrystalline phases in a thick layer adjacent to the p/i interface, or possibly when different phases co-exist locally at the p/i interface over different spatial regions of the same solar cell. Based on these considerations, one can understand a fill factor dependence on VOC that is U-shaped as in Fig. 7.25. A limitation to the performance of the solar cells with a nc-Si:H bottom cell arises due to the relatively low VOC-FF product for cells in which nc-Si:H dominates at the p/i interface. For example, assuming a desired VOC of 1.4 V with 0.85 V arising from the a-Si:H and 0.55 V from the nc-Si:H solar cell, the average fill factor is ∼0.25, suggesting that for this VOC value, a transition between phases occurs in the i-layer adjacent to the p/i interface region. Improvements in the fill-factor to a value of 0.55 require a considerable reduction in VOC to the maximum of ∼1.25 V which would be consistent with ∼0.85 V arising from the a-Si:H and ∼0.4 V arising from the nc-Si:H. This low VOC of 0.4 V associated with the addition of the bottom cell may be attributable to a poor quality recombination junction, an incompletely optimized p-layer, or to p/i interface recombination due to either void structures or residual amorphous phase at the interface. In fact, the dielectric functions of Fig. 7.15 indicate a high void fraction in the fully nc-Si:H phase, and the structural evolution of Fig. 7.21 indicates a 0.5–0.6 nc-Si:H material fraction near the p/i interface with the remaining material being amorphous. The real time SE results provide insights into various process changes that may assist in the improvement of the VOC-FF product. A graded H2-dilution starting from a value greater than R = 40 to promote initial crystallite nucleation in conjunction with a decrease in R continuously as the film increases in thickness would ensure that a high volume fraction crystallite phase forms immediately from the p/i interface and grain boundaries remain appropriately passivated with a-Si:H as the film evolves in thickness. The eventual evolution and coalescence of crystallites even for R = 2 would seem to suggest that in the grading process R can be reduced to this low value to ensure grain boundary passivation with thin a-Si:H material;

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however, the problem associated with such low R values is the spatial non-uniformity. Thus, the final R value used in grading must avoid this problem. It is possible that spatial non-uniformity can be mitigated with a reduction in total gas pressure or an increase in SiH4 gas flow in order to avoid SiH4 depletion, reducing the gas residence time in the plasma. Next the effect of preparing bottom cell p-layers at the elevated rf plasma power density of P = 192 mW/cm2 on the tandem device performance parameters will be discussed, as shown in Figs. 7.24 and 7.25. For the elevated power level, three solar cell structures with R = 10, 20, and 40 i-layers were prepared. As noted previously, the overall performance of these cells and its dependences on R and VOC are similar to those of the cell structures with the bottom cell nc-Si:H p-layer prepared at the lower rf plasma power density of P = 128 mW/cm2. Incorporation of the P = 192 mW/cm2 p-layer results in an improvement in device performance at R = 20, which for all depositions is the minimum R value while ensuring a dominant nanocrystallite phase in the p/i interface region over much of the deposition area. Apparently, the bottom cell p-layer deposited at higher power promotes greater nanocrystallinity in the i-layer region adjacent to the p-layer, leading to improvements in the maximum values of all three solar cell performance parameters. This also suggests the possibility that future improvements enhancing the nanocrystallinity of the bottom cell p-layer can lead to improvements in the i-layer and the overall cell performance. This expectation relies on the conclusions of previous real time SE studies that demonstrate the clear effects of the phase of the underlying film on the phase evolution of the overlying film [11, 12].

7.3

7.3.1

Mapping SE for Correlations with Device Performance: Optimization of nc-Si:H n-Layers in a-Si:H Solar Cells General Strategy and Approaches

Two approaches exist for developing new or improved processes in thin film PV manufacturing. For thin film technologies that have yet to reach maturity, small area photovoltaic devices are optimized on the laboratory scale. Once an optimum process is achieved with sufficiently high performance, then scale up of the process is desired. The goal in scale-up is to maintain the high performance achieved in the laboratory, and this requires spatial uniformity in thickness and materials properties over large areas. Alternatively for mature technologies, one can seek to improve overall performance and yield at full-scale. In either approach, mapping SE over large areas can be a valuable capability, as it avoids cutting full-scale panels into individual pieces for single point measurements [34, 35]. Mapping SE can involve mounting the ellipsometer heads on a translation stage and either scanning the panel in two dimensions typically off-line [34] or exploiting the motion of the panel

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on-line and scanning the panel in one dimension [35]. In this way, mapping SE is ideally suited for measuring non-uniformities in thickness or dielectric function and then evaluating their impact on current collection based on a summation of absorbances computed from each of the active layers. Both ex situ multiple angle of incidence and in situ real time SE approaches have been developed for extracting both structural information and complex dielectric functions. Ex situ multi-angle SE has its limitations when more than a few structural parameters must be extracted in addition to an unknown dielectric function determined point by point versus photon energy. In many circumstances, these limitations can be overcome by expressing the dielectric function in an analytical form. As demonstrated in Sect. 7.2, real time SE also overcomes these limitations for even the most complicated multilayer structures through measurements of each deposited film for a continuous array of thicknesses. By studying each film as it is deposited, the structure and point-by-point dielectric function of a film growing uniformly with accumulated thickness can be extracted by multi-time analysis. For films having dielectric functions that are graded with accumulated thickness, virtual interface analysis becomes possible. Considering the limiting case of a film with perfect spatial uniformity, then ex situ mapping SE provides no further data analysis power over ex situ SE at a single location. If the film is spatially non-uniform with a sufficient range in thickness, however, analysis of data simultaneously at several locations spanning the range in thickness, i.e. multi-spot analysis, becomes equivalent to multi-time analysis. Thus, the requirement in multi-spot analysis is equivalent to that in multi-time analysis, namely that the dielectric function must not vary as the thickness changes. Next a simple example will be shown to demonstrate the similarity between mapping and real time SE analysis results in studies of Si:H. Figure 7.26 shows maps of the bulk and surface roughness layer thicknesses for an intrinsic a-Si:H film deposited on a 15 cm × 15 cm TEC™ 15 glass substrate. The topmost layer on the glass substrate is SnO2:F in this case having a surface roughness layer thickness of ∼472 Å. As a result, the a-Si:H film acquires roughness imposed by conformal coverage of the underlying SnO2:F surface as the a-Si:H layer is deposited. The clear statistical relation of Fig. 7.27 is found between the surface roughness and the bulk layer thicknesses from the two maps of Fig. 7.26. This behavior is consistent with substrate-induced roughness on the a-Si:H which is smoothened with increasing thickness due to the effects of conformal coverage and diffusion of film precursors on the a-Si:H surface before their incorporation into the bulk. An exponential decay of surface roughness to a stable value versus bulk thickness is predicted as a result of precursor surface diffusion [36, 37]. In fact, the data exhibit reasonable agreement with this behavior, as shown by the solid line in Fig. 7.27, which is the best two-parameter fit to an equation of the form ds = k1 + 472 Å − k1 expð − adb Þ, where k1 is the final stable roughness value in

the limit of thick film deposition. Thus, the fit is constrained such that ds ðdb = 0 ÅÞ = 472 Å, which is an area average of the starting roughness on the SnO2:F, as measured before the deposition. A second set of correlations of the

292 Fig. 7.26 Maps of the a bulk thickness and b surface roughness layer thickness obtained by ex situ mapping SE for an a-Si:H i-layer deposited on a 15 cm × 15 cm TEC™ 15 glass substrate. The two curves (top and right) show the thickness variations along the X and Y axes

Fig. 7.27 Correlation between the surface roughness and bulk layer thicknesses for the a-Si:H i-layer obtained from ex situ mapping SE analysis of a coated TEC™ 15 glass panel 15 cm × 15 cm in size. The solid line is an exponential decay function designed to fit the data while passing through ds = 472 Å at db = 0 Å, which is the thickness of the surface roughness measured for the SnO2:F before a-Si:H deposition

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structural properties obtained by mapping SE is provided at the very end of this section. These latter correlations provide insights into nanocrystallite evolution with bulk layer thickness. Finally, if an array of small area cells is fabricated starting from a spatially non-uniform multilayer stack, then the performance parameters of the solar cells can be correlated with the structural and optical properties as determined by mapping SE [15, 16]. In this way, process-property-performance correlations can be established based on a single deposition. With fabrication of the array of small area devices in parallel using appropriate masks, and subsequent automated mapping and device analysis, fine tuning of the performance optimum is possible in a single deposition. This methodology will be demonstrated in the next sub-sections. With intentional spatial non-uniformities built into a process and the ability to characterize those non-uniformities by mapping SE, rapid combinatorial approaches for optimization are possible.

7.3.2

Dielectric Function Determination for nc-Si:H n-Layers

Single junction p-i-n a-Si-H solar cells have been fabricated on 15 cm × 15 cm TEC™ 15 glass in order to evaluate effects of n-layer crystallinity on device performance [16]. The a-Si:H cells under investigation apply the same basic process as those used in the top cell of the tandem a-Si-H/nc-Si-H solar cells of the previous section. The n-layers have been prepared on a-Si:H i-layers using a range of H2dilution ratios, 90 ≤ R ≤ 150, in an attempt to control the crystallite evolution and its volume fraction for the range of n-layer thicknesses of interest used in solar cells. Because the n-layer film nucleates from an a-Si:H i-layer, the initial stage of growth consists of an a-Si:H n-layer that is relatively uniform with depth. As the film thickness increases, however, nanocrystals nucleate, increase in size and coalesce according to a growth evolution diagram similar in form to that of Fig. 7.22a. The initial discussion will focus on the determination of the dielectric functions of the amorphous and stable nanocrystalline phases of the n-layer including analyses of these spectra in terms of analytical models. Figures 7.28 and 7.29 show structural schematics used for determination of the dielectric functions in the amorphous and stable nanocrystalline stages of n-layer evolution. A simplified sample configuration was used to ensure a smoother i-layer surface and more accurate dielectric functions. In the amorphous growth stage, multi-time analysis is performed, and the resulting point-by-point dielectric functions can be fit using the Cody-Lorentz oscillator model with A, Γ, E0, Eg, and Ep as free parameters and with the constant offset ε1o set to unity. The final results depicting the dielectric functions of the a-Si:H phases for the series of n-layers are shown in Fig. 7.30, presented as the best fit analytical expressions. Figure 7.31 depicts an example of the more challenging procedure used for dielectric function

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Fig. 7.28 Schematic of a single phase a-Si:H n-layer deposited on a thermally oxidized crystalline silicon wafer, pre-coated with an a-Si:H i-layer, as used for real time SE. This structure enables simulation of n-layer deposition in the solar cell configuration

Fig. 7.29 Schematic of an n-layer that is non-uniform in thickness, initially growing as a-Si:H as in Fig. 7.28, nucleating nanocrystals, and finally becoming stable nc-Si:H at the surface

determination of the stable phase nc-Si:H, in this case nc-Si:H deposited with R = 80 [23]. In Fig. 7.31, an average MSE between the data and best fit is given versus a trial value of ds appropriate for the time of nanocrystallite contact, which occurs at the surface smoothening onset, as will be demonstrated in the next sub-section. Each trial value generates a different nc-Si:H dielectric function for use in a virtual interface analysis, in which case the EMA with volume fractions of amorphous, nanocrystalline, and void components, fa, fnc, and fv, is applied to obtain the dielectric function evolution for the top 10 Å of the bulk n-layer. The minimum average MSE occurs at ds = 100 Å, which gives the correct dielectric function for the nc-Si:H via inversion of SE data at the nanocrystallite contact point (maximum ds). The Fig. 7.31 inset gives the best fit nc-Si:H dielectric function obtained through point-by-point analysis with ds = 100 Å along with that of a-Si:H from the same deposition. Figure 7.32 shows the dielectric functions of the stable

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Fig. 7.30 Dielectric functions at 200 °C presented as the best fit analytical expressions for n-type a-Si:H materials obtained in the initial growth stage at four different hydrogen dilution ratios. The dielectric functions were modeled assuming a single Cody-Lorentz oscillator along with ε1o , an energy-independent contribution to the real part of ε

Fig. 7.31 Average mean square error (MSE) versus a trial value for the surface roughness thickness. The inset shows the amorphous (broken lines) and nanocrystalline (solid lines) complex dielectric functions ε obtained at 200 °C for an R = 80 n-type Si:H film, as determined by virtual interface analysis of real time SE data [16]

nc-Si:H for the same set of depositions as in Fig. 7.30, applying the MSE minimization procedure of Fig. 7.31 for each. The Cody-Lorentz parameters used to model the dielectric functions of the amorphous phase of the n-layer before the nanocrystallite nucleation transition are plotted versus the H2-dilution ratio in Fig. 7.33 [26]. In fact, two sets of parameters

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Fig. 7.32 The dielectric functions at 200 °C for nanocrystalline Si:H n-layers prepared using different H2dilution ratios along with the dielectric function at 200 °C for single crystalline silicon for comparison

are presented, the first with ε1o as a variable and the second with ε1o fixed at unity. The clearest parameter variation is observed in the bandgap, which increases monotonically as expected with the H2-dilution ratio. The same trend is obtained for both sets of dielectric function parameters. Another trend is an increase in Γ with increasing H2-dilution, which is opposite to the trends observed for a-Si:H i and p-layers. Such an effect may occur if the phosphorus atom incorporation increases with H2 dilution. The Cody-Lorentz parameters shown in Fig. 7.33 are plotted versus their bandgaps, as presented in Fig. 7.34 (points). Linear fits are also provided in the figure, in order to generate a parameterization for a-Si:H n-layers based on a single bandgap variable. It should be emphasized that the n-layer parameters are relevant for the substrate temperature of 200 °C. An adjustment to room temperature can be applied based on the assumption that the temperature dependences of the parameters for the n-layers are the same as those for i-layers [27]. This adjustment results in the solid lines in Fig. 7.34, blue-shifted relative to the 200 °C results. The dot-dashed lines in Fig. 7.34 are results for a set of p-layers deposited on i-layers in which case the parameters are also corrected for the substrate temperature. The dotted lines in Fig. 7.34 are the relationships reported by Ferlauto et al. for a-Si1-xGex:H (left) and a-Si1-xCx:H (right) i-layers at room temperature [26]. The results for the amplitude show consistent behavior for n and p layers that is nearly a continuation of the a-Si1-xGex:H i-layer trend of Ferlauto et al. The behaviors of the other three parameters differ between the n and p layers. Such differences for the

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Fig. 7.33 Dielectric function parameters for a-Si:H n-layers measured at 200 °C and plotted versus the H2-dilution ratio. For the solid and open symbols, the parameters derive from an analytical form of a single Cody-Lorentz oscillator with variable and fixed ε1o , respectively

n-layer include (i) an increasing Γ with bandgap similar to the a-Si1-xCx:H i-layers, but differing from the a-Si:H p-layers; (ii) an increasing E0 with bandgap, an expected trend, but one that differs from both the a-Si1-xCx:H i-layers and the a-Si:H p-layers; and finally, (iii) a weakly decreasing Ep with bandgap, a somewhat unexpected trend, and one that differs from the i and p layers. The results tend to suggest that the n-layers exhibit less disorder than the a-Si1-xCx:H i-layers and the a-Si:H p-layers, but that the disorder increases with increasing bandgap. The dielectric functions of Fig. 7.32 for the nc-Si:H phases of the n-layers were parameterized as described in Sect. 7.2.3 by using three modified Lorentz oscillators that share a common bandgap. The common bandgap was fixed at 1.069 eV for all dielectric functions, since this value is the bandgap of single crystal Si at 200 °C and also can be assigned as the bandgap of the nc-Si:H phases of the n-layers. The ten Lorentz oscillator parameters Aj, E0,j, Γj, including the offset ɛ1o are given in Table 7.6, obtained by fitting the nc-Si:H dielectric functions of the n-layers. These results have been summarized as the diamond-shaped data points in Figs. 7.10, 7.11, and 7.12 along with those of the nc-Si:H p-layers. Table 7.7 shows the results

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Fig. 7.34 Dielectric function parameters for a-Si:H n-layers measured at 200 °C and plotted versus the fitted bandgap. The parameters derive from an analytical form of a single Cody-Lorentz oscillator along with ε1o which was fixed at unity. The solid lines shifted to higher bandgap result from corrections of the elevated temperature trends to those appropriate for room temperature (20 °C) measurement of the n-layers. The dot-dashed lines are the trends for p-layers from Sect. 7.2, and the dotted lines are the trends for i-layers from Ferlauto et al. [26]

Table 7.6 Parameters used in an expression that represents the dielectric functions at 200 °C for the nanocrystalline Si:H phase of n-layers, as described by three Lorentz oscillators modified by a common indirect bandgap, along with an energy-independent contribution to ε1 R

ɛ1o

Modified Lorentz oscillators A (eV) Γ (eV)

80

1.716 ± 0.116

90

1.526 ± 0.218

100

1.438 ± 0.087

150

1.470 ± 0.010

13.253 44.472 19.881 17.291 55.770 11.411 11.687 65.178 14.968 15.800 71.089 13.509

± ± ± ± ± ± ± ± ± ± ± ±

3.688 5.763 3.084 5.757 8.059 2.419 2.443 5.185 2.912 2.570 5.332 2.874

0.597 0.948 1.787 0.920 1.091 1.209 0.678 1.103 1.493 0.721 1.210 1.500

± ± ± ± ± ± ± ± ± ± ± ±

E0 (eV) 0.061 0.088 0.175 0.097 0.075 0.130 0.057 0.047 0.129 0.049 0.052 0.160

3.671 4.120 4.923 3.664 4.206 5.211 3.608 4.174 5.115 3.537 4.167 5.224

± ± ± ± ± ± ± ± ± ± ± ±

Eg (eV) 0.018 0.015 0.120 0.045 0.017 0.042 0.016 0.007 0.048 0.013 0.008 0.047

1.069

1.069

1.069

1.069

of an analysis of the n-layer nc-Si:H dielectric functions using a model having four free parameters, including the variables fv, E0,2, Γ2, and ε1o , as described in Sect. 7.2.3, for a MSE comparison with the more general model having ten free

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parameters. Also included are the void fraction and MSE obtained by a single-parameter EMA analysis. The material of lowest void fraction from Sect. 7.2.3 was used as the density reference in Table 7.7, namely the p-layer fabricated with R = 225, Tsub = 120 °C, and P = 128 mW/cm2. Clearly the fit becomes poorer as the number of free parameters is reduced; however, the relatively small increase in MSE with the elimination of six free parameters appears to justify the parameter reduction method of Sect. 7.2.3. Such parameter reduction is likely to be needed when analyzing such films by ex situ SE in multilayer stacks. It should be pointed out, however, that these results are valid for the measurement temperature of 200 °C. For ex situ SE applications, data at room temperature for each sample would be needed. Alternatively, adjustments may be applied to shift the parameter values to those relevant for the desired temperature of measurement. The only available guidance for doing this is described in a previous study in which the temperature coefficients of eight modified-Lorentz parameters are reported (including the common value of Eg, but not the parameters of A3, E0,3, and Γ3, due to the limited spectral range of that study) [20]. Such adjustments would shift each value and affect the correlations reported here.

7.3.3

Growth Evolution Diagram for nc-Si:H n-Layers

Figure 7.35 depicts the evolution of surface roughness layer thickness and the nanocrystalline volume fraction versus bulk layer thickness for the n-type Si:H films deposited with H2-dilution flow ratios of R = 50, 80, and 100. These results were deduced from global MSE minimization as shown in Fig. 7.31 combined with virtual interface analyses over the mixed-phase growth regimes [16]. To extract the nanocrystalline Si:H volume fraction, the dielectric function of the outerlayer in the virtual interface analysis is modeled using the EMA as a mixture of a-Si:H, nc-Si:H, and void. The deposition rate is an outcome of the virtual interface analysis and values obtained in the amorphous and nanocrystalline growth stages, as well as an average throughout the deposition are shown in Fig. 7.36a. For the films prepared with R = 80 and 100, both amorphous-to-(mixed-phase) and (mixed-phase)to-nanocrystalline transitions can be clearly identified on the surface roughness evolution plots of Fig. 7.35. For the film prepared with R = 50, however, a weak smoothening effect was observed indicating amorphous Si:H growth for much of the deposited range of bulk layer thickness. The surface roughness on this R = 50 film was found to increase after the bulk layer thickness reached ∼820 Å, which indicates the film is undergoing the transition to mixed-phase material near this bulk thickness. Using such results obtained at different H2-dilution ratios R, a growth evolution diagram for the PECVD n-type Si:H can be generated [11]. In the diagram shown in Fig. 7.36b, the three phase evolution regions of amorphous, mixed phase, and nanocrystalline Si:H can be readily identified. These regions are separated by the two phase transitions designated as [a → (a + nc)] and [(a + nc) → nc], where

80

90

100

150

200

200

200

R

200

n-layer

Tsub (°C)

32

32

32

32

P (mW/ cm2)

1.835 ± 0.085

1.523 ± 0.057

1.382 ± 0.044

1.855 ± 0.089

ε1o

1.209 ± 0.008

1.065 ± 0.005

1.125 ± 0.005

1.001 ± 0.008

4.145 ± 0.003

4.202 ± 0.002

4.212 ± 0.002

4.141 ± 0.003

0.011 ± 0.001

0.039 ± 0.002

0.058 ± 0.001

0.097 ± 0.001

1.069

1.069

1.069

1.069

Eg (eV)

9.062

6.329

5.305

8.222

MSE

0.027 ± 0.003

0.060 ± 0.002

0.135 ± 0.002

0.146 ± 0.003

16.039

8.978

11.601

18.023

MSE

fv

fv

Γ 2 (eV) E0,2 (eV)

One parameter model

Four parameter model

6.635

4.890

2.689

6.968

MSE

Ten parameter model

Table 7.7 Summary of fitting results for the nanocrystalline Si:H phase of a series of n-layers using a four-parameter model including ε1o , Γ2 , E0,2, and fv. The other six parameters associated with the ten-parameter model were either fixed or linked to one of these four parameters through the expressions in Figs. 7.10, 7.11, and 7.12. A comparison of the MSE’s for the one, four, and ten parameter models is included

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Fig. 7.35 Surface roughness layer thickness ds and nanocrystalline Si:H volume fraction fnc plotted versus bulk layer thickness for R = 50, 80, and 100 Si:H n-layers. Depositions were performed on substrates consisting of thermally oxidized crystalline silicon wafers coated with intrinsic a-Si:H to simulate the p-i-n solar cell structure, but with a smoother surface

(a + nc) represents the mixed phase material. Contour lines of different nanocrystallite volume fractions are given as well, which can serve as a guide for solar cell fabrication in terms of the crystallite content at the surface of the n-layer. In addition to the surface roughness layer thickness, deposition rate of the outerlayer, and the nanocrystalline Si:H volume fraction of the outerlayer, the relative void volume fraction of the outerlayer serves as a fitting parameter in the SE model used for virtual interface analysis. The void fraction is a relative value since no voids are assumed in the determination of the single phase amorphous and nanocrystalline Si:H dielectric functions used in the EMA. Thus, these dielectric functions may incorporate voids implicitly that are not accounted for in the EMA analysis, existing not only in the single phase materials but also in the two-component composites. In Fig. 7.37, the relative void volume fraction is plotted as a function of the nanocrystalline Si:H volume fraction for the n-layers prepared at different H2dilution ratios. By definition, the relative void volume fractions in the Si:H films are negligible in the initial stage when the nanocrystalline Si:H volume fraction is near zero. The film prepared at R = 150 is an exception, however. The large initial void volume fraction of this film is due to an [a → (a + nc)] phase transition occurring for a very thin (∼45 Å) amorphous Si:H layer. Thus, the dielectric function of the amorphous phase could not be accurately obtained for this n-layer. As a result, the dielectric function of the pure amorphous phase used in the virtual interface analysis of the R = 150 deposition is the one obtained from the R = 100 deposition, which evidently has a lower void volume fraction than the amorphous phase of the

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Fig. 7.36 a Deposition rates versus hydrogen dilution ratio R = [H2]/[SiH4] for Si:H n-layers. For R ≥ 80, the rates include those for the individual amorphous and nanocrystalline phases as well as an average throughout the deposition. b Growth evolution diagram for PECVD n-type Si:H thin films as deposited on a-Si:H i-layers, depicting the thicknesses of the a → (a + nc) transition (squares) identified from the onset of roughening and the (a + nc) → nc transition (right-pointing triangles) identified from the maximum in the surface roughness where the nanocrystalline volume fraction reaches unity. Contours defining constant volume fractions of the nanocrystalline phase are included. The horizontal line shows the 250 Å target thickness of the n-layer in the devices. The vertical lines show the R values explored in device studies designed to achieve a range of nanocrystalline volume fractions at the n-layer surface

R = 150 film. Regardless of this issue, the relative void volume fraction begins to increase and reaches its maximum when the nanocrystalline volume fraction is in the range from 0.15 to 0.26. Finally, the relative void fraction returns to zero by definition when stable phase nanocrystalline Si:H evolves. The cone angle and the nucleation density can be calculated from (7.7) and (7.8) using structural information deduced from the real time SE data analyses of Fig. 7.35. Figure 7.38 shows these results as functions of the H2-dilution ratio. Results for the p-layers deposited on i-layers at different R values are also included

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Fig. 7.37 Relative void volume fraction versus nanocrystalline volume fraction obtained by virtual interface analysis of n-layer depositions on substrates consisting of thermally oxidized crystalline silicon wafers coated with layers of intrinsic a-Si:H

for comparison. The cone half angle can be deduced not only from the surface roughness evolution via (7.7), but also from the ratio of amorphous and nanocrystalline Si:H deposition rates Ra/Rnc according to [23, 38]: θ = cos − 1 ðRa ̸Rnc Þ.

ð7:9Þ

Considering first the results for the cone angles of the n and p-layers in Fig. 7.38, these values increase with increasing R. This can be attributed to a higher growth rate ratio of the nanocrystalline phase relative to the amorphous phase. The cone angles deduced from the growth rate ratio are considerably higher, however. In fact, Fig. 7.38 Results for the cone half angle θ and nucleation density Nd plotted versus the H2-dilution ratio R used in the deposition of a series of Si:H n-layers. Cone half angles were determined from the changes in the bulk and surface roughness layer thicknesses [filled squares, (7.7)] as well as from the of deposition rate ratio [filled circles, (7.9)]. Corresponding results for the p-layers of Sect. 7.2 are also included for comparison (open symbols)

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at the highest R = 150, the growth rate difference would suggest almost immediate coalescence of crystallites. The cone angles of the n-layers from the surface roughness evolution as described by (7.7) are found to be consistent with the trend observed for the p-layers and are thus believed to be more reliable. Considering next the nucleation densities in Fig. 7.38, a monotonic increase is observed as the H2-dilution ratio increases over the full range from 80 to 150. For the n-layers deposited with R ≤ 100, the trend in nucleation density appears continuous with that of the p-layers. For the sample deposited with the highest dilution ratio of R = 150, however, a much higher nucleation density is observed for the n-layer. This indicates that, under these conditions, it is much easier to nucleate n-type nc-Si:H during n-layer deposition at high R than it is to nucleate p-type nc-Si:H.

7.3.4

Mapping Spectroscopic Ellipsometry of Solar Cell Structures

A 16 × 16 array of a-Si:H p-i-n dot cells has been fabricated onto 15 cm × 15 cm TEC™ 15 glass substrates using the n-layer process as described in the previous sub-sections. The n-layer H2-dilution ratio for this cell fabrication was R = 100 and the doping gas ratio [PH3]/[SiH4] was fixed at 0.0125; other n-layer deposition parameters include a substrate temperature of Tsub = 200 °C, a plasma power of P = 32 mW/cm2, and a total pressure of ptotal = 1.5 Torr. These are the same conditions as those used for the top cell n-layer applied in the tandem solar cell. Mapping SE was applied over the substrate area and (current-density)voltage (J-V) measurements were performed on the array of dot cells in order to correlate n-layer material properties from SE and solar cell performance from J-V, as well as to characterize the role of macroscopic non-uniformities [16]. By exploiting the observed property variations over the large areas, the goal of these correlations is to identify and understand the relationships between the basic n-layer material properties and the single junction solar cell performance. With an appropriate optical model yielding property maps for all the layers of the device structure, one can evaluate impacts of the non-uniformities on the performance of scaled-up solar modules. The mapping SE was performed from the film side and avoided the back contact dot cells. Thus, the topmost layer of the probed structure is the n-layer, which is analyzed using a two layer bulk/roughness model. Three maps of interest were obtained in the analysis. Figure 7.39a, b depict the maps of the n-layer bulk layer thickness and surface roughness thickness. Figure 7.39c depicts a map of the nanocrystalline volume fraction fnc associated with the bulk n-layer, which is modeled throughout its thickness as an effective medium mixture of a-Si:H, nc-Si:H, and void. A range of fnc ∼ 0.50–0.75 is observed for the bulk layer thickness range of db ∼ 265–300 Å. For this thickness range, the virtual interface analysis of

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Fig. 7.39 Maps of the Si:H n-layer a bulk c nanocrystalline volume fraction over a 13 structure incorporating an R = 100 n-layer. temperature of Tsub = 200 °C, a rf power ptotal = 1.5 Torr [16]

305

and b surface roughness layer thicknesses, and cm × 13 cm area for an a-Si:H p-i-n solar cell Other deposition parameters include a substrate of P = 32 mW/cm2, and a total pressure of

Figs. 7.35 and 7.36 yields top surface fnc values in the range of fnc ∼ 0.73–0.86. The lower values for the maps are consistent to some extent with depth averaging of the nanocrystalline content within the n-layer. Given the cone-like geometry of nucleation, however, the deduced average leads to a result more closely characteristic of the top surface rather than a true average throughout the n-layer thickness. This is possible due to an apparently higher weighting effect of the surface in the analysis using a single bulk layer model for the graded n-layer. Two observations can be made from the thickness map of Fig. 7.39a. First, the center area of the sample exhibits a greater bulk layer thickness compared with the outer area. Such a non-uniformity pattern may be caused by edge effects, meaning that the center of the anode exhibits a higher plasma density in the PECVD process relative to the edge. Second, a slight shift is observed in the non-uniformity pattern to the right side of the substrate. Apparently this asymmetry is caused by the gas flow pattern in the deposition chamber. Because the gas flow is from right to left, SiH4 depletion is more likely to occur on the left side. Hence, a thinner n-layer on the left side of the substrate appears correlated with a locally increasing R value and

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a decreasing deposition rate. Due to the local increase in R, a slightly thicker surface roughness layer is observed on the left side of the substrate, as shown in Fig. 7.39b. Because film growth is within the mixed phase (a-Si:H + nc-Si:H) region for the bulk thickness of ∼270 Å, a higher hydrogen dilution ratio R will enhance nanocrystallite formation resulting in a rougher surface and a higher nanocrystalline fraction on the left side of the maps, as shown in Fig. 7.39c. In addition, it can be observed from the maps that the two cathode openings used for real time SE monitoring significantly affect the film uniformity. The effect is largest on the right side of the substrate. These two openings in the cathode appear to reduce the plasma density. As a result, the n-layer bulk and surface roughness thicknesses, as well as the nanocrystalline volume fraction in this region are observed to be lower than the surrounding substrate area.

7.3.5

Property-Performance Correlations for Solar Cells

The open-circuit voltage and fill-factor performance maps of solar cells incorporating R = 100 n-layers are shown in Fig. 7.40a, b [16]. It can be seen that the outer area gives higher VOC and FF. The two circular patterns of reduced VOC are observed on the map of Fig. 7.40a. These patterns are again caused by the openings in the cathode plate for real time SE monitoring. Cell performance is best evaluated from the VOC × FF product rather than from the efficiency, since the short circuit current depends sensitively on the device structure (single vs. tandem) and the back-reflector design. This product is mapped in Fig. 7.40c and shows that the elevated performance occurs in an area that surrounds the center with the highest performance along the right edge. The performance parameters presented in Figs. 7.40 are difficult to interpret without correlations with fundamental properties to be presented next. In Fig. 7.41a, the product of open circuit voltage and fill factor is presented versus the n-layer nanocrystalline volume fraction. The significant scatter in the data and variation in the envelope implies that for a given n-layer nanocrystalline volume fraction, other p, i, and n-layer properties may be varying such as their thicknesses, optical bandgaps, and depth profiles in fnc. In addition, localized defects such as substrate contaminants and plasma particulates can generate shunting, leading to low shunt resistance at isolated locations on the device structure surface and reduced performance that also contributes to the scatter. The two cells with the highest individual open circuit voltage and fill factor were obtained at n-layer nanocrystalline volume fractions from 0.58 to 0.6. All data for the VOC-FF product in Fig. 7.41a were fit using a second order polynomial function of nanocrystalline volume fraction (broken line parabola) which serves to identify the nanocrystalline volume fraction at which the maximum performance occurs on a statistical basis. This optimum nanocrystalline fraction for a given parameter is shown at upper right on the plots. Thus, on a statistical basis, the maximum product of open circuit voltage and fill factor is observed to occur at a nanocrystalline

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Fig. 7.40 Maps of the solar cell performance parameters of a VOC, b FF, and c VOC-FF product over a 13 cm × 13 cm substrate area for a-Si:H p-i-n devices incorporating an R = 100 n-type Si:H layer. Other n-layer deposition parameters include a substrate temperature of Tsub = 200 °C, a plasma power of P = 32 mW/cm2, and a total pressure of ptotal = 1.5 Torr

volume fraction of ∼0.57, which is very close to the values for the two cells with the highest product of open circuit voltage and fill factor. One can now understand why the optimized performance on the map of Fig. 7.40c is located in the outer ring of the anode where the nanocrystalline fraction lies near ∼0.6. In order to achieve the optimum conditions at the center of the anode, R must be decreased to reduce the volume fraction of nanocrystalline Si:H there. Alternatively, the gas pressure can be reduced to avoid depletion at the center of the anode. This latter change in the deposition process may enable the higher performance achieved on the right side of the maps to extend across the full electrode. Thus, the correlations between the solar cell and basic property maps provide directions for optimization of cell performance and improved uniformity. Figure 7.41b, c illustrate the correlations of solar cell performance with the n-layer bulk and surface roughness thicknesses, respectively. Cells with the highest VOC-FF product span the range of 275–290 Å in the bulk layer thickness and 95– 100 Å in the surface roughness thickness. For all data in Fig. 7.41b, c, the VOC-FF product was fit using second order polynomial functions of n-layer bulk and surface

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Fig. 7.41 Product of the key performance parameters of open circuit voltage and fill factor (VOC × FF) correlated with the properties of the top-most R = 100 n-layer including a near-surface nanocrystalline volume fraction fnc, b bulk layer thickness, and c surface roughness layer thickness over a 13 cm × 13 cm area for a-Si:H p-i-n solar cells. The blue and green vertical broken lines identify the cells with the highest VOC and highest FF, respectively. The parabolic trends given by the red broken lines are the best fits to the complete data sets with the n-layer property at the maximum given at upper right. The solid lines define the maximum performance envelopes as guides to the eye

roughness thicknesses (broken line parabolas) which identify the structure at which the maximum performance occurs on a statistical basis. The thicknesses at which the maxima in the polynomial functions occur are entered into the upper right corner of each figure panel. On a statistical basis, the optimum VOC × FF product occurs at ∼280 Å bulk layer thickness and ∼90 Å surface roughness layer thickness. Figure 7.42a, b show plots of n-layer surface roughness thickness and top surface nanocrystalline volume fraction correlated with the bulk layer thickness. As expected for Si:H deposition in the mixed-phase stage of the growth evolution diagram, both the surface roughness and the nanocrystalline volume fraction increase monotonically as the bulk layer thickness increases. Figure 7.42c shows the close linear dependence of the n-layer surface roughness thickness on the n-layer nanocrystalline volume fraction. As the nanocrystalline component increases in volume fraction, protrusions above the surface increase in height, and Fig. 7.42c suggests a precise geometric relationship between the two. As a result, the optimum

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Fig. 7.42 Correlations of a surface roughness thickness with bulk thickness; b nanocrystalline volume fraction with bulk thickness; and c surface roughness thickness with nanocrystalline fraction, all from mapping SE for the R = 100 n-layer. The results are given for a 13 cm × 13 cm substrate area covered by a 16 × 16 array of a-Si:H p-i-n solar cells. The highest performing cells are given within the squares. The solid lines in the upper panel are the trends expected using a geometric model of nanocrystallites growing as inverted cones with spherical caps. The angle θ is the cone half-angle, and dbi is the bulk layer thickness at the onset of the [a → (a + nc)] transition. The same geometric model is used to describe the data sets in (b) and (c). In (b), K is a constant that depends on the area distribution of conical nanocrystallites; K = 4 and K = 3.46 represent nanocrystallites on square and hexagonal close-packed grids. Nd in the bottom panel is the nucleation density of nanocrystallites

nanocrystalline volume fraction of fnc ∼ 0.6 from the statistical analysis corresponds to an optimum surface roughness thickness in the range of 95–105 Å. In the following paragraphs, the geometric relationships apparent in the three panels of Fig. 7.42 will be explored.

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Considering Fig. 7.42a first, a positive correlation between the surface roughness and bulk layer thicknesses is expected within a cone growth model for the nanocrystallites. This relationship is given by ds = ðsec θ − 1Þðdb − dbi Þ + dsi ,

ð7:10Þ

where db and ds are the bulk and surface roughness layer thicknesses for the n-layer, dbi and dsi are the corresponding values at the a → (a + nc) transition, and θ is the nanocrystallite cone half-angle. Thus, dbi is the bulk layer thickness from which the apices of inverted cones originate, and dsi is the surface roughness thickness at this bulk layer thickness. This expression is based on a model in which the conical nanocrystalline inclusions grow at a faster rate than the surrounding amorphous phase. Inverted nanocrystalline conical structures result in spherically-shaped cone caps of radius rc = Δdb + Δds , where Δdb = db − dbi and Δds = ds − dsi . In this simple geometric model, the cone caps form the roughness layer. For a thickness-independent cone half-angle θ and fixed values of dbi and dsi, the ds versus db relationship in (7.10) is linear. The slope of the topmost solid line in Fig. 7.42a suggests that the maximum roughness thickness envelope reflects the development of nanocrystalline cones with a fixed half-angle θ of 46° as the n-layer bulk thickness increases. This result from the mapping SE is reasonably close to the value of θ = 41◦ from the real time SE analysis of Fig. 7.38. By assigning a surface roughness layer thickness dsi at the onset of the amorphous-to-(mixed-phase) transition, then the n-layer bulk thickness dbi at the transition can be determined from the intercept of the top solid line. The initial roughness layer thickness dsi is set to 40 Å, based on Fig. 7.27, which shows the roughness layer thickness for a 3400 Å i-layer deposited on TEC™ 15. The parallel lines in Fig. 7.42a are associated with a fixed θ = 46◦ and a range of dbi values from ∼123 Å to 186 Å, with the majority of the data points lying within the dbi range of 123–144 Å. The lower limit result of dbi ∼ 123 Å is in close consistency with the growth evolution diagram in Fig. 7.36b which exhibits dbi = 120 Å, supporting the simple geometric interpretation of (7.10). The results also support an interpretation in which the spatial variation in data corresponds predominantly to the variation in bulk layer thickness, but with similar dbi and conical geometry. This also suggests that the samples on the upper side of the distribution are from the center of the electrode where the real time SE information of Figs. 7.35 and 7.36 is obtained. A linear trend through the highest density of data points in Fig. 7.42a (dot-dashed line) yields a cone angle of 43.5°, which is closer to the real time SE result of 41°; however, this line extrapolates to dbi = 107 Å, which is lower than the real time SE result of 120 Å for the a → (a + nc) transition. Irrespective of the line selection in Fig. 7.42a, there is agreement to within 10–20% in the geometric nucleation parameters between the real time SE and mapping SE. The data points also appear to be bounded on the lower roughness side by a line with θ = 65◦ and dbi = 248 Å. This would imply that in regions where crystallites nucleate at

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larger db, the cone angles are larger. Such behavior would be inconsistent with Fig. 7.38, however. A more likely interpretation of the spread in Fig. 7.42a is that the data just above the lower limit line correspond to the combination of a lower cone angle (shallower slope) and a larger dbi value (up to ∼186 Å, as indicated), behavior that would be consistent with Fig. 7.38. Based on the assumption that the measured nanocrystalline volume fraction is associated with the top surface, the following relationship can be derived: fnc =

πðdb − dbi Þ2 Kðdbc − dbi Þ2

,

ð7:11Þ

where dbc is the bulk layer thickness at nuclei contact and K is a constant that depends on the nuclei distribution. For nucleation on square and hexagonal close packed grids, K = 4 and 3.464, respectively. For the deposition of interest with R = 100, real time SE analysis led to dbc = 305 Å, as shown in Fig. 7.36b. Figure 7.42b shows the results of (7.11) using dbc = 305 Å as a fixed parameter and dbi = 123 Å, which defines the upper envelope in Fig. 7.42a and is closely consistent with the a → (a + nc) transition from real time SE. For these fixed parameters, the range of K values from 3.464 to 4, i.e. a variation in the packing of nuclei, can account for most devices of the distribution. Variations in the dbi and dbc values may also contribute to the variations, but to a lesser extent in the former case, as shown by the corresponding result in Fig. 7.42b for dbi = 144 Å. More generally a closer fit to the data set is possible based on the assumption that the packing of conical structures is between that of the relatively open square grid and the close-packed patterns, i.e. for K ∼ 3.7. The close linear relationship between the surface roughness thickness and the nanocrystalline volume fraction as shown in Fig. 7.42c can be understood by the same assumptions and geometric model that explain the variations in Fig. 7.42a, b. In this case, the relationship between ds and fnc is given by:  ds =

fnc π Nd

1

̸2

tan½ð1 ̸2Þ θ + dsi ,

ð7:12Þ

where Nd is the nucleation density. A calculation of ds versus fnc is presented in Fig. 7.42c based on the selection of dsi = 40 Å from Fig. 7.27 and θ = 46◦ from Fig. 7.42a. In this case, the data are consistent with a nucleation density of 8.82 × 1010 cm−2 which yields the solid line result in Fig. 7.42c and a reasonable fit to the data. This nucleation density is very close to that obtained from the real time SE experiment of 8 × 1010 cm−2. Thus, we conclude that the thickness non-uniformity studied by mapping SE yields geometric information consistent with real time SE and the geometric aspects of nucleation and growth can be determined from mapping SE alone.

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The highest performance solar cells overall are given within the squares on the three panels of Fig. 7.42. For these cells, the n-layer structural parameters are best described by db ∼ 290 Å, ds ∼ 100 Å, and fnc ∼ 0.60, the latter representing the nanocrystalline volume fraction at the near surface of the n-layer. Among the complete collection of cells, these highest efficiency devices exhibit the lowest surface roughness thickness and the lowest nanocrystallite volume fraction for the given bulk layer thickness. This observation suggests that these cells exhibit characteristics consistent with a lower R value with a larger dbi value relative to the devices that come from the electrode center. Thus, the highest efficiency devices exhibit thinner n-layers with lower crystallite contents, which then take longer to nucleate. The overall results suggest that a lower R and/or lower rf plasma power, as well as lower pressure to avoid depletion, would enable high performance cells over the full substrate area.

7.4

Summary

For ex situ spectroscopic ellipsometry (SE) analysis, the primary difficulty lies in distinguishing between layers whose optical properties are similar over the accessible spectral range, for example, intrinsic and doped layers of the same material. Real time SE is an important capability at both laboratory and production scales that can overcome such difficulties. One of the challenges in real time SE data interpretation relates to the modification of the underlying film structure by the depositing film. The simplest form of such modification occurs inevitably as the voids in the surface roughness on the underlying layer are filled with depositing material [17]. Analysis of real time SE data involves simultaneously analyzing the pairs of spectra collected at a number of times during which the bulk layer thickness increases typically linearly with time after the interaction with the underlying material has completely stabilized [18]. The standard multi-time analysis approach requires a dielectric function for the growing film that is thickness-independent at least until the latest time used in the multi-time analysis. The results of the analysis include the point-by-point dielectric function versus photon energy and the structural parameters of bulk and surface roughness layer thicknesses versus time. For films that are non-uniform with depth and can be broken into a small number of layers, individual multi-time analyses can be performed. It is more likely, however, that the non-uniformity leads to a graded layer structure. In this circumstance, a virtual interface analysis procedure is most appropriate for extracting the dielectric function of an outermost layer as the film grows, burying the history of the graded layer in a pseudo-substrate [25]. In this study both approaches for real time SE analysis have been applied to the successive layers of a p-i-n tandem solar cell consisting of a-Si:H/nc-Si:H top/ bottom cells [14–16]. Multi-time analysis has been applied to the top cell i-layer

7 Real Time and Mapping Spectroscopic Ellipsometry …

313

and virtual interface analysis has been applied to the top cell n-layer. Results in correlation with device performance include the optimization of both the crystalline content of the top cell n-layer [15, 16] and the promotion of nucleation and coalescence of the bottom cell nc-Si:H p and i-layers [14, 15]. Growth evolution diagrams have been developed and presented for the top cell n-layer and the bottom cell i-layer. These diagrams provide the bulk layer thickness at which the transition to stable-phase nc-Si:H occurs, plotted as a function of the H2-dilution ratio, which is the primary deposition variable that controls the phase of the film [11]. In addition, contour lines of constant crystalline content are also included on the diagrams, enabling optimization of doped layer processes. Of particular interest in this study is the structural development of the bottom cell i-layer which exhibits a continuous evolution from mixed-phase Si:H to nanocrystalline Si:H in a process that depends sensitively on the underlying p-layer structure. The real time SE results for the i-layer phase evolution provide a clear understanding of the device performance variations and directions for improvement. Another goal of interest in these studies is the development of analytical expressions for the dielectric functions of the nc-Si:H layers with approaches for correlating photon energy-independent parameters so that the number of free parameters can be reduced. Simple oscillator models for nc-Si:H over the photon energy range from 1 to 6 eV require ten variables. Here relationships have been developed that suggest four variables may be sufficient for this purpose. The studies reviewed here suggest promising approaches for developing physics-based dielectric function parameterizations for doped and nanocrystalline Si:H layers that enable characterization of material properties beyond simply the thickness in complicated multilayer stacks. Finally, the power of ex situ mapping SE has been described in this review with a focus on the characterization and optimization of Si:H thin films [15, 16]. All large area thin film multilayers exhibit some degree of spatial non-uniformity in the thicknesses of the component films. In Si:H-based photovoltaic structures whose properties evolve with bulk layer thickness, for example, the surface roughness layer thickness or the nanocrystalline content, multi-spot analysis exploiting the thickness non-uniformity is found to give equivalent information to multi-time and virtual interface analyses in real time SE [23, 25]. In this review, the Si:H n-layer in single junction p-i-n solar cells has been studied with the ultimate goal of incorporating such devices as the top cell in a tandem. Applying mapping SE data, nanocrystallite nucleation densities and cone angles can be determined from plots that correlate the n-layer surface roughness thickness, surface nanocrystallite content, and the bulk layer thickness. In correlations of solar cell performance with processing-property information that reflects the growth evolution diagram, one can identify the structural profile, from the i/n-interface to the back contact, that serves to optimize the solar cell. When intentional spatial non-uniformities are incorporated into multiple layers of the same device structure and mapped by ex situ SE, optimization using combinatorial methods is possible. This is a potentially important future direction that may expedite the development of time consuming process-property-performance correlations.

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References 1. E.A. Schiff, S. Hegedus, X. Deng, in Handbook of Photovoltaic Science and Engineering, 2nd edn., ed. by A. Luque, S. Hegedus (Wiley, New York, NY, 2011), Chapter 12, p. 487 2. A. Shah (ed.), Thin Film Silicon Solar Cells (CRC, Boca Raton, FL, 2010) 3. J. Meier, S. Dubail, R. Platz, P. Torres, U. Kroll, J.A. Anna Selvan, N. Pellaton Vaucher, C. Hof, D. Fischer, H. Keppner, R. Fluckiger, A. Shah, V. Shklover, K.D. Ufert, Solar Energy Mater. Solar Cells 78, 35 (1997) 4. A. Shah, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz, U. Graf, Solar Energy Mater. Solar Cells 78, 469 (2003) 5. X. Cao, J.A. Stoke, J. Li, N.J. Podraza, W. Du, X. Yang, D. Attygalle, X. Liao, R.W. Collins, X. Deng, J. Non-Cryst. Solids 354, 2397 (2008) 6. B. Yan, G. Yue, L. Sivec, J. Yang, S. Guha, C.-S. Jiang, Appl. Phys. Lett. 99, 113512 (2011) 7. T. Matsui, H. Sai, K. Saito, M. Kondo, Prog. Photovolt.: Res. Appl. 21, 1363 (2013) 8. H. Sai, T. Matsui, K. Matsubara, M. Kondo, I. Yoshida, IEEE J. Photovolt. 4, 1349 (2014) 9. M.A. Green, K. Emery, Y. Hishikawa, W. Warta, E.D. Dunlop, D.H. Levi, A.W.Y. Ho-Baillie, Prog. Photovolt.: Res. Appl. 25, 3 (2017) 10. O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, Solar Energy Mater. Solar Cells 62, 97 (2000) 11. R.W. Collins, A.S. Ferlauto, G.M. Ferreira, C. Chen, J. Koh, R.J. Koval, Y. Lee, J.M. Pearce, C.R. Wronski, Solar Energy Mater. Solar Cells 78, 143 (2003) 12. L.R. Dahal, J. Li, J.A. Stoke, Z. Huang, A. Shan, A.S. Ferlauto, C.R. Wronski, R.W. Collins, N.J. Podraza, Solar Energy Mater. Solar Cells 129, 32 (2014) 13. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, Chichester, UK, 2007) 14. Z. Huang, L.R. Dahal, M.M. Junda, P. Aryal, S. Marsillac, R.W. Collins, N.J. Podraza, IEEE J. Photovolt. 5, 1516 (2015) 15. Z. Huang, in Spectroscopic Ellipsometry Studies of Thin Film a-Si:H/nc-Si:H Micromorph Solar Cell Fabrication in the p-i-n Superstrate Configuration. Ph.D. Dissertation (University of Toledo, Toledo, OH, 2016) 16. Z. Huang, L.R. Dahal, C. Salupo, A.S. Ferlauto, N.J. Podraza, R.W. Collins, in Conference Record of the 39th IEEE Photovoltaics Specialists Conference, Tampa, FL, 16–21 June 2013 (IEEE, New York, 2013), p. 1788 17. J. Koh, Y.W. Lu, S. Kim, J.S. Burnham, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 67, 2669 (1995) 18. I. An, Y.M. Li, H.V. Nguyen, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 59, 2543 (1991) 19. B. Johs, J.S. Hale, Phys. Stat. Solidi (a) 205, 715 (2008) 20. R.W. Collins, A.S. Ferlauto, in Handbook of Ellipsometry, ed. by H.G. Tompkins, E.A. Irene (William Andrew, Norwich, NY, 2005), Chapter 2, p. 93 21. M.M. Junda, A. Shan, P. Koirala, R.W. Collins, N.J. Podraza, IEEE J. Photovolt. 5, 307 (2015) 22. A.S. Ferlauto, G.M. Ferreira, R.J. Koval, J.M. Pearce, C.R. Wronski, R.W. Collins, M.M. Al-Jassim, K.M. Jones, Thin Solid Films 455–456, 665 (2004) 23. J.A. Stoke, L.R. Dahal, J. Li, N.J. Podraza, X. Cao, X. Deng, R.W. Collins, in Conference Record of the 33rd IEEE Photovoltaics Specialist Conference, San Diego, CA, 11–16 May 2008 (IEEE, New York, 2008), Paper 413 24. D.E. Aspnes, J. Opt. Soc. Am. A 10, 974 (1993) 25. S. Kim, R.W. Collins, Appl. Phys. Lett. 67, 3010 (1995) 26. A.S. Ferlauto, G.M. Ferreira, J.M. Pearce, C.R. Wronski, R.W. Collins, X. Deng, G. Ganguly, J. Appl. Phys. 92, 2424 (2002) 27. T. Yuguchi, Y. Kanie, N. Matsuki, H. Fujiwara, J. Appl. Phys. 111, 083509 (2012) 28. K. von Rottkay, M. Rubin, Materials Research Society Symposium Proceedings: Thin Films for Photovoltaic and Related Devices, vol. 426 (MRS, Warrendale, PA, 1996), p. 449

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29. J. Chen, J. Li, D. Sainju, K.D. Wells, N.J. Podraza, R.W. Collins, in Conference Record of the IEEE 4th World Conference on Photovoltaic Energy Conversion 2006, Waikoloa, HI, 7–12 May 2006 (IEEE, New York, NY, 2006), p. 475 30. N.J. Podraza, C.R. Wronski, M.W. Horn, R.W. Collins, Materials Research Society Symposium Proceedings: Amorphous and Polycrystalline Thin-Film Silicon Science and Technology—2006, vol. 910 (MRS, Warrendale, PA, 2006), p. 259 31. H.V. Nguyen, R.W. Collins, Phys. Rev. B 47, 1911 (1993) 32. P. Etchegoin, J. Kircher, M. Cardona, Phys. Rev. B 47, 10292 (1993) 33. P. Lautenschlager, M. Garriga, L. Viña, M. Cardona, Phys. Rev. B 36, 4821 (1987) 34. Z. Huang, J. Chen, M.N. Sestak, D. Attygalle, L.R. Dahal, M.R. Mapes, D.A. Strickler, K.R. Kormanyos, C. Salupo, R.W. Collins, in Conference Record of the 35th IEEE Photovoltaic Specialists Conference, Honolulu, HI, 20–25 June 2010 (IEEE, New York, NY, 2010), p. 1678 35. J. Chen, P. Koirala, C. Salupo, R.W. Collins, S. Marsillac, K.R. Kormanyos, B.D. Johs, J.S. Hale, G.L. Pfeiffer, in Conference Record of the 38th IEEE Photovoltaic Specialists Conference, Austin, TX, 3–8 June 2012 (IEEE, New York, NY, 2012), p. 377 36. R.W. Collins, B.Y. Yang, J. Vac. Sci. Technol. B 7, 1155 (1989) 37. Y.A. Kryukov, N.J. Podraza, R.W. Collins, J. Amar, Phys. Rev. B 80, 085403 (2009) 38. C.W. Teplin, C.-S. Jiang, P. Stradins, H.M. Branz, Appl. Phys. Lett. 92, 093114 (2008)

Part II

Optical Data of Solar-Cell Component Materials

Chapter 8

Inorganic Semiconductors and Passivation Layers Akihiro Nakane, Shohei Fujimoto, Gerald E. Jellison Jr., Craig M. Herzinger, James N. Hilfiker, Jian Li, Robert W. Collins, Takashi Koida, Shinho Kim, Hitoshi Tampo and Hiroyuki Fujiwara Abstract The dielectric functions and optical constants of various inorganic solar-cell materials, a total of 58 semiconductors, are summarized. The semiconductor materials described here include the group-IV (Si, Ge, and a-Si:H), III–V (GaAs, GaP, InP, InAs, and AlAs), II–VI (CdTe, CdS, ZnTe, ZnSe, and ZnS), I–III–VI2 (CuInSe2 and CuGaSe2) and I2–II–IV–VI4 (Cu2ZnSnSe4, Cu2ZnSnS4 and Cu2ZnGeSe4) semiconductors. For a-Si:H, Cu(In,Ga)Se2 and Cu2ZnSn(S,Se)4based alloys, the variation of the optical constants with alloy composition is presented. This chapter also provides the optical properties of crystalline Si passivation layers (SiN, SiO2, Al2O3, and Ga2O3), which are necessary for optical simulation of solar cells. Furthermore, it is established in this chapter that the dielectric functions of numerous direct and indirect transition semiconductors can be parameterized almost perfectly by assuming several transition peaks calculated from the Tauc-Lorentz model. In this chapter, the parameterization results for all the 58 semiconductors are also summarized. For the passivation layers, the parameterization results obtained using the Sellmeier model are shown.

A. Nakane ⋅ S. Fujimoto ⋅ H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] G. E. Jellison Jr. Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA e-mail: [email protected] C. M. Herzinger ⋅ J. N. Hilfiker J.A. Woollam Co., Inc., 645 M Street, Suite 102, Lincoln, NE 68508, USA J. Li ⋅ R. W. Collins University of Toledo, Toledo, OH 43606, USA T. Koida ⋅ S. Kim ⋅ H. Tampo Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Japan © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_8

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Introduction

The basic potential of a solar cell material is ultimately governed by the absorption characteristics and thus the absorption spectrum of the semiconducting light absorber is of paramount importance. Moreover, for optical device simulations and ellipsometry characterization of solar cell structures, the optical constants of all the solar-cell component layers are necessary. In this chapter, for the purpose of spectroscopic ellipsometry (SE) characterization and device simulation, the tabulated optical constants of various inorganic semiconductors at room temperature are provided. In particular, for most semiconductor materials, refractive index n and extinction coefficient k are shown in a wavelength (λ) range of 300–1200 nm with steps of 5 nm (300–400 nm) and 10 nm (400–1200 nm). From these numerical values, the dielectric function (ε = ε1 − iε2) can be calculated quite easily according to ε1 = n2 − k2 and ε2 = 2nk (see Sect. 1.2.1). The λ value can also be converted to energy (E) by E = 1239.8/[λ (nm)] eV [(1.3)]. From the value of k, the absorption coefficient (α) in the unit of cm−1 can further be obtained by α = 4πk ⋅ 107 ̸ (λ [nm]) [(1.17)]. In the tabulated data, the absolute k value is denoted as “0” when there is no observable light absorption, even though materials may have very small k (or α) values in a certain E region. It should be noted that the SE sensitivity for α is generally limited to ∼500 cm−1 and low α values in a range of 10−2–102 cm−1 in this chapter have been determined by incorporating results obtained from transmission measurements (see Fig. 8.3 in Vol. 1). Unfortunately, the tabulated data are sometimes insufficient for more complete SE analysis or optical simulation. Accordingly, almost all the dielectric functions of inorganic semiconductors were parameterized assuming the Tauc-Lorentz model described by (1.19)–(1.20). The Tauc-Lorentz model was developed originally to express the dielectric function of amorphous materials, but this model is found to be quite effective for the complete parameterization of crystalline-phase semiconductor materials, which exhibit complex transition peaks in the visible region. It should be emphasized that the Tauc-Lorentz model is used solely to establish the optical database of numerous solar-cell component layers. The main advantage of the Tauc-Lorentz model is the feature that ε2 = 0 in an energy region below the band gap (Eg): i.e., E ≤ Eg [see (1.19)]. Through careful modeling, we established that all the direct and indirect transition semiconductors can be modeled almost perfectly by combining several Tauc-Lorentz transition peaks. In particular, by incorporating Tauc-Lorentz peaks with very small amplitudes, the α spectra of various inorganic semiconductors are reproduced in a quite wide range of α = 10−2–106 cm−1 using only one dielectric function model. From the Tauc-Lorentz parameters described in this chapter, (ε1, ε2), (n, k) and α values at arbitrary λ and E can be calculated quite easily. In this chapter, the ε2 spectrum of semiconductor materials is modeled simply as a sum of the Tauc-Lorentz peaks:

8 Inorganic Semiconductors and Passivation Layers m

ε2 ðEÞ = ∑

321

Aj Cj E0, j ðE − Eg, j Þ2

j = 1 ½ðE 2

− E0,2 j Þ2 + Cj2 E2 E

ð8:1Þ

.

As confirmed from the above equation, a single Tauc-Lorentz peak is expressed by four parameters: i.e., the amplitude parameter Aj, broadening parameter Cj, peak transition energy E0,j, and optical gap Eg,j of the jth Tauc-Lorentz peak (see Fig. 1.19). From the parameters of (8.1), ε1(E) can then be calculated from the Kramers-Kronig integration of each Tauc-Lorentz peak: 0 2 B ε1 ðEÞ = ∑ @ε1, j ð∞Þ + P π j=1 m

Z∞ Eg

1 ′

′

E ε2, j ðE Þ ′C dE A, E ′2 − E2

ð8:2Þ

where ε1,j(∞) represents a constant contribution to ε1(E) at high energies. The second term in the parenthesis shows the Kramers-Kronig integration of the jth Tauc-Lorentz peak [ε2,j(E′) in (8.2)]. As shown in (8.2), when a dielectric function is modeled by combining several Tauc-Lorentz peaks, ε1(E) is calculated as a sum of the ε1 contributions obtained from each Tauc-Lorentz peak (see the example of Si shown in Fig. 8.1). The Kramers-Kronig integration of (8.2) can be performed rather easily using the exact equation described in (1.20). In addition, the calculation example of the Tauc-Lorentz model has been indicated in (1.26). A free software described in Sect. 2.7 can further be applied to calculate the dielectric function from the Tauc-Lorentz model parameters listed in this chapter. In the actual parameterization of the dielectric function using (8.1) and (8.2), the dielectric function fitting is performed only for ε2(E) at the initial stage. In particular, this ε2(E) fitting is carried out using a rather limited energy range of ∼0.1 eV near Eg. After a satisfactory fitting is obtained, the fitting energy region is expanded slightly toward the higher energy and the ε2(E) fitting is performed again by adding new Tauc-Lorentz oscillators. This process is repeated until the intended energy region of the ε2 spectrum is fitted. During the consecutive fittings, the Tauc-Lorentz peak parameters in the lower energy region are fixed and only the parameters of new peaks are adjusted in some cases. In the next step, the ε1(∞) parameter is determined from the ε1-spectrum fitting by fixing the ε2-spectral parameters. In the final fitting performed for both ε1(E) and ε2(E), all the parameters are adjusted again, except for the parameters of the small amplitude peaks located near Eg. The above scheme is critical to obtain the reasonable fitting in a wide α range of 10−2–106 cm−1. The parameterization of all the semiconductor dielectric functions, described in this chapter, was implemented by the group of Gifu University (A. Nakane and S. Fujimoto), unless otherwise noted. For optically transparent passivation layers, on the other hand, the following Sellmeier model was used.

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n2 ðλÞ = 

B1 λ2 B 2 λ2 B 3 λ2      +1 + + λ2 − C 1 λ2 − C 2 λ2 − C3

ð8:3Þ

In this model, there are a total of six parameters (B1, B2, B3, C1, C2, C3) and the n spectrum can be calculated quite easily from these parameter values while assuming k = 0 (see Sect. 1.2.3).

8.2

Optical Data of Inorganic Semiconductors and Passivation Layers

8.2.1

Si

The optical data of a single Si crystal at room temperature (295 K = 22 °C) are shown. These data correspond to those in Figs. 8.2 and 8.3 (Chap. 8 in Vol. 1). Near the indirect band edge (700–1170 nm), the absorption coefficient or extinction coefficient depend significantly on temperature. If the sample temperature is different from 22 °C, then the expressions of (8.9) and (8.10) found in Chap. 8 (Vol. 1) should be used for the absorption coefficient (Tables 8.1 and 8.2).

Table 8.1 Tauc-Lorentz parameters of (8.1) and (8.2) for Si Peak j j j j j j j j j j j

= = = = = = = = = = =

1 2 3 4 5 6 7 8 9 10 11

A (eV) −4

5.446 × 10 7.068 × 10−3 0.817 0.381 0.837 712.571 237.142 25.134 29.911 102.277 0.435

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

0.028 0.215 1.611 0.700 0.488 0.216 0.881 0.738 0.402 1.064 0.243

1.157 1.177 1.632 1.861 2.810 3.368 3.531 4.015 4.277 5.158 5.349

1.107 1.029 1.148 1.429 1.658 3.107 2.746 1.705 1.751 4.311 1.510

0.724 0 0 0 0 0 0 0 0 0 0

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Fig. 8.1 a Dielectric function and optical constants and b absorption coefficient of a Si single crystal at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. In (b), the Eg position of crystalline Si, determined from theoretical analysis (Sect. 8.2.3 in Vol. 1), is indicated

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Table 8.2 Optical constants of Si. The optical data of Fig. 8.1 obtained by G. E. Jellison are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286

1.190 1.213 1.234 1.262 1.291 1.319 1.362 1.414 1.468 1.533 1.587 1.641 1.665 1.673 1.673 1.663 1.660 1.658 1.663 1.669 1.683 1.702 1.721 1.749 1.778 1.815 1.853 1.905 1.971 2.051 2.157 2.295 2.459 2.653 2.873 3.111 3.363 3.624 3.93

3.067 3.089 3.119 3.151 3.182 3.229 3.282 3.325 3.368 3.397 3.400 3.388 3.376 3.369 3.370 3.398 3.429 3.476 3.526 3.593 3.671 3.753 3.839 3.927 4.014 4.114 4.222 4.337 4.458 4.585 4.722 4.853 4.973 5.090 5.182 5.257 5.306 5.344 5.334

328 330 332 334 336 338 340 342 344 346 348 350 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 410 420

5.155 5.164 5.193 5.203 5.234 5.256 5.28 5.302 5.355 5.398 5.449 5.498 5.569 5.665 5.782 5.921 6.086 6.279 6.473 6.656 6.812 6.908 6.924 6.877 6.771 6.662 6.522 6.399 6.295 6.192 6.087 5.986 5.889 5.81 5.736 5.657 5.595 5.316 5.097

3.111 3.075 3.05 3.019 2.996 2.981 2.958 2.935 2.931 2.928 2.931 2.924 2.937 2.952 2.965 2.961 2.928 2.860 2.737 2.552 2.312 2.026 1.724 1.434 1.186 0.997 0.843 0.732 0.645 0.575 0.515 0.464 0.424 0.389 0.357 0.328 0.304 0.217 0.168

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010

3.874 3.856 3.840 3.824 3.810 3.796 3.783 3.770 3.759 3.747 3.736 3.726 3.716 3.707 3.699 3.691 3.683 3.676 3.669 3.662 3.655 3.649 3.642 3.635 3.630 3.624 3.619 3.614 3.609 3.604 3.600 3.595 3.591 3.587 3.583 3.579 3.575 3.572 3.568

1.59 × 10−2 1.51 × 10−2 1.44 × 10−2 1.36 × 10−2 1.23 × 10−2 1.17 × 10−2 1.14 × 10−2 1.06 × 10−2 9.50 × 10−3 8.93 × 10−3 8.39 × 10−3 7.86 × 10−3 7.37 × 10−3 6.89 × 10−3 6.43 × 10−3 5.99 × 10−3 5.58 × 10−3 5.18 × 10−3 4.80 × 10−3 4.43 × 10−3 4.09 × 10−3 3.73 × 10−3 3.45 × 10−3 3.15 × 10−3 2.87 × 10−3 2.60 × 10−3 2.35 × 10−3 2.12 × 10−3 1.89 × 10−3 1.68 × 10−3 1.49 × 10−3 1.31 × 10−3 1.14 × 10−3 9.81 × 10−4 8.39 × 10−4 7.07 × 10−4 5.89 × 10−4 4.83 × 10−4 3.88 × 10−4 (continued)

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Table 8.2 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326

4.256 4.531 4.744 4.882 4.957 5.001 5.02 5.033 5.044 5.051 5.051 5.055 5.056 5.059 5.065 5.077 5.099 5.109 5.122 5.135

5.257 5.090 4.864 4.647 4.420 4.240 4.069 3.930 3.811 3.706 3.610 3.535 3.464 3.402 3.348 3.304 3.251 3.210 3.175 3.137

430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620

4.924 4.786 4.675 4.573 4.493 4.413 4.346 4.289 4.237 4.19 4.147 4.108 4.072 4.039 4.01 3.982 3.957 3.934 3.912 3.892

0.133 0.109 9.30 × 7.80 × 6.70 × 5.93 × 5.23 × 4.66 × 4.17 × 3.76 × 3.37 × 3.02 × 2.73 × 2.52 × 2.36 × 2.24 × 2.11 × 2.00 × 1.87 × 1.73 ×

1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.565 3.562 3.559 3.556 3.553 3.550 3.547 3.545 3.542 3.540 3.537 3.535 3.532 3.530 3.528 3.526 3.524 3.522 3.520

3.06 2.36 1.77 1.30 8.66 6.68 5.09 3.92 3.00 2.23 1.61 1.15 8.23 5.58 3.51 1.93 0 0 0

8.2.2

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

× × × × × × × × × × × × × × × ×

10−4 10−4 10−4 10−4 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−6 10−6 10−6 10−6

Ge

To express the dielectric function of a Ge single crystal, two separate data sets are used depending on the energy region: (i) Data of G. E. Jellison, Jr. [1] for 1.94 < E ≤ 3.9 eV, (ii) Unpublished data of C. M. Herzinger [2] for 0.2 < E ≤ 1.94 eV and E > 3.9 eV. The result of [2] above was determined from a multiple data set analysis. The data sets came from values compiled in a handbook edited by E. D. Palik [3] originally from ellipsometry results [4], from another compilation [5], and from transmittance results [6]. This work also uses a parametric optical constant model [7] that allows a simultaneous analysis of different experimental results with dissimilar wavelength ranges and values. The resulting optical constants provide wide spectral coverage, continuity, and Kramers-Kronig consistency. The functional form employs Gaussian broadening and the superposition of subsections organized by critical point structures. To help reconcile differences among the experiments, the analysis model for the ellipsometric data set included an overlayer adjustment. The same basic procedure was also used for GaAs, InAs, GaP, and AlSb in this chapter (Tables 8.3 and 8.4).

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Fig. 8.2 Dielectric function and absorption coefficient of a Ge single crystal at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.3 Tauc-Lorentz parameters of (8.1) and (8.2) for Ge Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j j j j j j j

1.474 × 10−3 0.017 30.354 5.368 × 10−4 0.095 0.097 6.790 × 10−3 6.468 95.588 26.781 45.081 190.066 9.627 17.285 3.688 3.797

0.113 0.135 0.048 1.164 0.054 0.011 0.436 0.945 0.209 0.224 1.113 1.394 0.684 0.340 0.244 0.939

0.675 0.743 0.803 0.808 0.812 0.842 1.014 1.030 2.116 2.319 2.475 3.315 4.003 4.199 4.325 5.662

0.517 0.549 0.795 0.453 0.643 0.800 0.499 0.792 1.826 1.864 0.945 2.322 0.942 2.475 0.900 0.900

1.104 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

= = = = = = = = = = = = = = = =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

8 Inorganic Semiconductors and Passivation Layers

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Table 8.4 Optical constants of Ge. The optical data of Fig. 8.2, obtained by G. E. Jellison and C. M. Herzinger, are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580

3.969 4.003 4.017 4.022 4.019 4.031 4.038 4.056 4.067 4.082 4.101 4.115 4.137 4.166 4.190 4.217 4.232 4.240 4.247 4.236 4.223 4.170 4.130 4.099 4.102 4.121 4.158 4.208 4.273 4.360 4.460 4.592 4.756 4.957 5.136 5.226 5.300 5.420 5.635

3.749 3.517 3.340 3.199 3.098 3.009 2.932 2.864 2.802 2.749 2.697 2.654 2.610 2.561 2.514 2.459 2.401 2.344 2.285 2.229 2.181 2.122 2.102 2.116 2.143 2.177 2.214 2.256 2.291 2.331 2.366 2.395 2.414 2.378 2.242 2.106 2.019 1.964 1.837

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100

4.942 4.909 4.877 4.847 4.819 4.793 4.768 4.745 4.723 4.701 4.681 4.662 4.644 4.627 4.610 4.595 4.579 4.565 4.551 4.538 4.525 4.513 4.502 4.490 4.479 4.469 4.459 4.449 4.440 4.431 4.422 4.414 4.405 4.397 4.390 4.382 4.375 4.368 4.361

0.401 0.380 0.362 0.344 0.328 0.313 0.300 0.287 0.275 0.264 0.253 0.243 0.234 0.226 0.217 0.210 0.202 0.196 0.189 0.183 0.177 0.171 0.166 0.161 0.156 0.152 0.147 0.143 0.139 0.135 0.131 0.128 0.124 0.121 0.118 0.115 0.112 0.109 0.107

1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1940 1980 2020 2060 2100 2140 2180

4.268 4.261 4.254 4.248 4.243 4.238 4.234 4.232 4.230 4.231 4.236 4.249 4.263 4.247 4.225 4.210 4.200 4.191 4.183 4.176 4.170 4.164 4.159 4.154 4.149 4.145 4.141 4.137 4.133 4.130 4.126 4.123 4.117 4.112 4.106 4.102 4.097 4.093 4.090

7.71 × 10−2 7.55 × 10−2 7.41 × 10−2 7.31 × 10−2 7.24 × 10−2 7.19 × 10−2 7.17 × 10−2 7.18 × 10−2 7.22 × 10−2 7.29 × 10−2 7.37 × 10−2 6.98 × 10−2 4.39 × 10−2 1.39 × 10−2 5.28 × 10−3 3.91 × 10−3 3.18 × 10−3 2.61 × 10−3 2.16 × 10−3 1.80 × 10−3 1.50 × 10−3 1.26 × 10−3 1.07 × 10−3 9.02 × 10−4 7.62 × 10−4 6.44 × 10−4 5.43 × 10−4 4.57 × 10−4 3.83 × 10−4 3.22 × 10−4 2.68 × 10−4 2.24 × 10−4 1.54 × 10−4 1.05 × 10−4 7.09 × 10−5 4.75 × 10−5 3.16 × 10−5 2.09 × 10−5 1.37 × 10−5 (continued)

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Table 8.4 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

590 600 610 620 630 640 650 660 670 680 690 700 710

5.796 5.791 5.710 5.608 5.494 5.403 5.307 5.229 5.164 5.110 5.062 5.018 4.979

1.548 1.241 1.011 0.851 0.734 0.665 0.607 0.565 0.530 0.500 0.472 0.446 0.422

1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1220 1240 1260

4.355 4.348 4.342 4.336 4.330 4.324 4.319 4.313 4.308 4.303 4.294 4.285 4.276

0.104 0.102 9.97 × 9.75 × 9.55 × 9.35 × 9.16 × 8.99 × 8.82 × 8.66 × 8.37 × 8.12 × 7.90 ×

2220 2260 2300 2340 2380 2420 2460 2500 2550 2600 2650 2700

4.086 4.083 4.080 4.077 4.074 4.071 4.069 4.067 4.064 4.061 4.059 4.057

8.99 5.85 3.81 2.47 1.61 1.04 6.72 4.37 2.56 1.48 8.35 0

8.2.3

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

× × × × × × × × × × ×

10−6 10−6 10−6 10−6 10−6 10−6 10−7 10−7 10−7 10−7 10−8

SiO2

Data from C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson [8]. The optical data have been extracted from SiO2 thermal oxides formed on crystalline Si (Tables 8.5 and 8.6).

Fig. 8.3 Refractive index spectrum of SiO2 thermal oxides at room temperature. The open circles show the reference data and the solid line indicates the refractive index spectrum calculated by the Sellmeier model of (8.3)

Table 8.5 Sellmeier parameters of (8.3) for SiO2 Material

B1

B2

B3

C1 (μm2)

C2 (μm2)

C3 (μm2)

SiO2

0.633

0.486

0.647

0.00449

0.0126

63.628

8 Inorganic Semiconductors and Passivation Layers

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Table 8.6 Refractive index of SiO2. The optical data reported by Herzinger et al. are shown (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.4936 1.4922 1.4909 1.4897 1.4885 1.4874 1.4863 1.4853 1.4844 1.4834 1.4826 1.4817 1.4810 1.4802 1.4795 1.4788 1.4781 1.4775 1.4769 1.4763 1.4757 1.4746 1.4736 1.4727 1.4719 1.4711

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.4703 1.4696 1.4690 1.4683 1.4678 1.4672 1.4667 1.4662 1.4657 1.4653 1.4649 1.4645 1.4641 1.4637 1.4634 1.4630 1.4627 1.4624 1.4621 1.4618 1.4616 1.4613 1.4610 1.4608 1.4606 1.4603

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.4601 1.4599 1.4597 1.4595 1.4593 1.4590 1.4589 1.4587 1.4585 1.4583 1.4581 1.4579 1.4578 1.4576 1.4575 1.4573 1.4571 1.4570 1.4568 1.4567 1.4565 1.4564 1.4562 1.4561 1.4559 1.4558

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4557 1.4555 1.4554 1.4553 1.4551 1.4550 1.4549 1.4547 1.4546 1.4544 1.4543 1.4542 1.4541 1.4539 1.4538 1.4537 1.4536 1.4534 1.4533 1.4532 1.4531 1.4529 1.4528

8.2.4

Al2O3

Data from G. Dingemans and W. M. M. Kessels [9]. The optical data have been extracted from an Al2O3 layer annealed at 400 °C. The Al2O3 sample was prepared by atomic layer deposition (Fig. 8.4, Tables 8.7 and 8.8).

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Fig. 8.4 Refractive index spectrum of Al2O3 at room temperature. The open circles show the reference data and the solid line indicates the refractive index spectrum calculated by the Sellmeier model of (8.3)

Table 8.7 Sellmeier parameters of (8.3) for Al2O3 Material

B1

B2

B3

C1 (μm2)

C2 (μm2)

C3 (μm2)

Al2O3

1.125

0.555

6.747

0.00242

0.0214

550.747

Table 8.8 Refractive index of Al2O3. The optical data reported by Dingemans et al. are shown (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380

1.6986 1.6961 1.6938 1.6916 1.6896 1.6876 1.6858 1.6841 1.6824 1.6809 1.6794 1.6780 1.6767 1.6754 1.6742 1.6731 1.6720

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620

1.6595 1.6584 1.6573 1.6564 1.6555 1.6546 1.6538 1.6531 1.6524 1.6517 1.6511 1.6505 1.6499 1.6493 1.6488 1.6483 1.6479

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880

1.6441 1.6437 1.6434 1.6432 1.6429 1.6426 1.6423 1.6421 1.6418 1.6416 1.6413 1.6411 1.6409 1.6407 1.6405 1.6402 1.6400

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140

n 1.6382 1.6380 1.6378 1.6377 1.6375 1.6373 1.6372 1.6370 1.6369 1.6367 1.6366 1.6364 1.6363 1.6361 1.6359 1.6358 1.6357 (continued)

8 Inorganic Semiconductors and Passivation Layers

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Table 8.8 (continued) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

385 390 395 400 410 420 430 440 450

1.6709 1.6699 1.6690 1.6680 1.6663 1.6647 1.6633 1.6619 1.6606

630 640 650 660 670 680 690 700 710

1.6474 1.6470 1.6466 1.6462 1.6458 1.6454 1.6450 1.6447 1.6444

890 900 910 920 930 940 950 960 970

1.6398 1.6396 1.6394 1.6393 1.6391 1.6389 1.6387 1.6385 1.6383

1150 1160 1170 1180 1190 1200

1.6355 1.6354 1.6352 1.6351 1.6349 1.6348

8.2.5

Ga2O3

Data from T. Koida, Y. Kamikawa-Shimizu, A. Yamada, H. Shibata and S. Niki [10]. The optical data have been extracted from an amorphous Ga2O3 layer prepared by room-temperature sputtering using a Ga2O3 target and Ar gas (Fig. 8.5, Tables 8.9 and 8.10).

Fig. 8.5 Dielectric function of Ga2O3 at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.9 Tauc-Lorentz parameters of (8.1) and (8.2) for Ga2O3 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2

3.838 241.918

0.669 0.009

5.010 5.803

2.999 5.058

2.725 0

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Table 8.10 Refractive index of Ga2O3. The optical data reported by Koida et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.113 2.096 2.081 2.069 2.057 2.048 2.039 2.029 2.017 2.013 2.008 2.002 1.998 1.996 1.995 1.985 1.982 1.980 1.977 1.974 1.970 1.964 1.959 1.955 1.957 1.954 1.943 1.935 1.929 1.925 1.922 1.917 1.921 1.917

0.015 0.013 0.012 0.011 0.01 0.009 0.008 0.007 0.008 0.006 0.005 0.004 0.004 0.004 0.002 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.914 1.912 1.911 1.909 1.908 1.907 1.905 1.904 1.903 1.902 1.901 1.900 1.900 1.899 1.898 1.898 1.897 1.896 1.895 1.897 1.896 1.895 1.894 1.895 1.892 1.892 1.892 1.891 1.889 1.897 1.895 1.887 1.886 1.888

0 0 0 0 0.001 0.002 0.002 0.002 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.005 0.005 0.005 0.005 0.004 0.005 0.006 0.006 0.007 0.008 0.007 0.006 0.009 0.005 0.005 0.012 0.013 0.008

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.889 1.898 1.894 1.897 1.897 1.898 1.895 1.895 1.895 1.897 1.897 1.897 1.897 1.895 1.896 1.893 1.896 1.893 1.894 1.895 1.893 1.897 1.896 1.892 1.896 1.898 1.896 1.897 1.893 1.889 1.895 1.897 1.897

0.010 0.004 0.006 0.004 0.006 0.007 0.005 0.006 0.014 0.004 0.003 0.004 0.006 0.004 0.004 0.009 0.004 0.003 0.003 0.003 0.001 0 0.001 0.002 0.001 0.001 0 0 0.001 0.001 0 0 0

8.2.6

SiN

Data from G. E. Jellison, Jr., F. A. Modine, P. Doshi and A. Rohatgi [11]. The optical data have been extracted from various SiN samples with different Eg, prepared by plasma-enhanced chemical vapor deposition (Tables 8.11, 8.12, 8.13, 8.14, 8.15 and 8.16).

8 Inorganic Semiconductors and Passivation Layers

333

Fig. 8.6 a Optical constants and b dielectric functions of various SiN layers having different Eg. The optical functions have been calculated from the Tauc-Lorentz parameters reported by Jellison et al.

Table 8.11 Tauc-Lorentz parameters of (8.1) and (8.2) for the SiN dielectric functions in Fig. 8.6, reported by Jellison et al. Eg (eV)

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

1.84 2.02 2.15 2.33 2.74

202 177 147 107 80

4.02 5.9 7.1 9.5 7.0

3.50 4.30 4.89 6.9 8.8

1.84 2.02 2.15 2.33 2.74

1 1 1 1 1

Table 8.12 Optical constants of SiN (Eg = 1.84 eV) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355

3.008 3.066 3.122 3.176 3.228 3.277 3.325 3.370 3.412 3.453 3.491 3.526

2.007 1.978 1.947 1.914 1.880 1.843 1.805 1.766 1.726 1.684 1.642 1.598

540 550 560 570 580 590 600 610 620 630 640 650

3.654 3.626 3.597 3.568 3.538 3.507 3.477 3.446 3.416 3.387 3.358 3.331

0.263 0.223 0.187 0.155 0.125 0.099 0.076 0.057 0.040 0.026 0.016 0.008

λ (nm) 880 890 900 910 920 930 940 950 960 970 980 990

n

k

3.069 0 3.064 0 3.059 0 3.055 0 3.050 0 3.046 0 3.042 0 3.038 0 3.035 0 3.031 0 3.028 0 3.024 0 (continued)

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Table 8.12 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.560 3.590 3.619 3.645 3.669 3.691 3.711 3.729 3.745 3.770 3.789 3.801 3.807 3.808 3.804 3.796 3.784 3.768 3.750 3.729 3.705 3.680

1.555 1.510 1.466 1.421 1.376 1.331 1.286 1.242 1.197 1.110 1.025 0.942 0.862 0.786 0.713 0.643 0.578 0.516 0.458 0.404 0.353 0.306

660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.305 3.281 3.260 3.242 3.226 3.211 3.198 3.186 3.174 3.163 3.153 3.144 3.135 3.127 3.119 3.112 3.105 3.098 3.092 3.086 3.080 3.074

0.003 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.021 3.018 3.015 3.012 3.010 3.007 3.004 3.002 2.999 2.997 2.995 2.993 2.991 2.989 2.987 2.985 2.983 2.981 2.979 2.977 2.976

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Table 8.13 Optical constants of SiN (Eg = 2.02 eV) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365

3.071 3.100 3.128 3.153 3.177 3.198 3.218 3.235 3.251 3.265 3.278 3.289 3.298 3.306

1.324 1.287 1.249 1.211 1.173 1.136 1.098 1.060 1.023 0.986 0.949 0.913 0.877 0.842

540 550 560 570 580 590 600 610 620 630 640 650 660 670

3.084 3.060 3.035 3.011 2.988 2.965 2.944 2.924 2.907 2.893 2.880 2.868 2.857 2.847

0.067 0.050 0.035 0.023 0.014 0.007 0.002 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010

2.736 0 2.734 0 2.731 0 2.728 0 2.725 0 2.723 0 2.721 0 2.718 0 2.716 0 2.714 0 2.712 0 2.710 0 2.708 0 2.706 0 (continued)

k

8 Inorganic Semiconductors and Passivation Layers

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Table 8.13 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.313 3.318 3.323 3.325 3.327 3.328 3.328 3.324 3.317 3.307 3.295 3.280 3.263 3.244 3.224 3.203 3.180 3.157 3.133 3.109

0.808 0.774 0.740 0.708 0.676 0.644 0.614 0.555 0.499 0.447 0.397 0.351 0.307 0.267 0.230 0.196 0.164 0.136 0.110 0.087

680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.838 2.830 2.822 2.815 2.808 2.801 2.795 2.789 2.784 2.779 2.774 2.769 2.765 2.761 2.757 2.753 2.749 2.746 2.743 2.739

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.704 2.703 2.701 2.699 2.698 2.696 2.695 2.693 2.692 2.691 2.689 2.688 2.687 2.686 2.685 2.684 2.683 2.681 2.680

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Table 8.14 Optical constants of SiN (Eg = 2.15 eV) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365

2.853 2.869 2.884 2.897 2.908 2.918 2.927 2.934 2.940 2.945 2.949 2.951 2.953 2.953

0.937 0.904 0.871 0.838 0.806 0.774 0.742 0.711 0.681 0.651 0.622 0.593 0.565 0.538

540 550 560 570 580 590 600 610 620 630 640 650 660 670

2.680 2.660 2.641 2.624 2.609 2.596 2.585 2.575 2.566 2.557 2.549 2.542 2.536 2.529

0.014 0.008 0.003 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010

2.456 0 2.454 0 2.452 0 2.450 0 2.448 0 2.446 0 2.445 0 2.443 0 2.442 0 2.440 0 2.439 0 2.437 0 2.436 0 2.435 0 (continued)

k

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Table 8.14 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.953 2.952 2.950 2.947 2.944 2.940 2.935 2.924 2.911 2.896 2.880 2.862 2.844 2.824 2.804 2.783 2.762 2.741 2.721 2.700

0.512 0.486 0.461 0.436 0.412 0.389 0.367 0.325 0.285 0.248 0.214 0.183 0.154 0.128 0.104 0.083 0.065 0.049 0.035 0.024

680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.524 2.518 2.513 2.508 2.504 2.499 2.495 2.492 2.488 2.484 2.481 2.478 2.475 2.472 2.470 2.467 2.465 2.462 2.460 2.458

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.433 2.432 2.431 2.430 2.429 2.428 2.427 2.426 2.425 2.424 2.423 2.422 2.421 2.420 2.420 2.419 2.418 2.417 2.417

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Table 8.15 Optical constants of SiN (Eg = 2.33 eV) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375

2.561 2.560 2.558 2.556 2.553 2.550 2.546 2.542 2.538 2.533 2.527 2.522 2.516 2.510 2.504 2.497

0.435 0.413 0.391 0.370 0.350 0.330 0.312 0.294 0.276 0.260 0.244 0.229 0.214 0.200 0.186 0.174

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690

2.278 2.270 2.264 2.257 2.252 2.246 2.242 2.237 2.233 2.229 2.225 2.222 2.219 2.216 2.213 2.210

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030

2.178 0 2.177 0 2.176 0 2.175 0 2.174 0 2.173 0 2.172 0 2.171 0 2.170 0 2.169 0 2.169 0 2.168 0 2.167 0 2.166 0 2.166 0 2.165 0 (continued)

k

8 Inorganic Semiconductors and Passivation Layers

337

Table 8.15 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.491 2.484 2.477 2.470 2.463 2.448 2.434 2.419 2.404 2.390 2.375 2.361 2.347 2.334 2.321 2.309 2.297 2.287

0.161 0.150 0.138 0.128 0.118 0.099 0.082 0.067 0.054 0.042 0.032 0.023 0.016 0.010 0.006 0.003 0.001 0

700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.208 2.205 2.203 2.201 2.199 2.197 2.195 2.193 2.191 2.190 2.188 2.187 2.185 2.184 2.182 2.181 2.180 2.179

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.164 2.164 2.163 2.163 2.162 2.161 2.161 2.160 2.160 2.159 2.159 2.158 2.158 2.158 2.157 2.157 2.156

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Table 8.16 Optical constants of SiN (Eg = 2.74 eV) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385

2.273 2.264 2.255 2.247 2.238 2.230 2.222 2.214 2.207 2.199 2.192 2.185 2.178 2.171 2.165 2.158 2.152 2.146

0.114 0.104 0.095 0.087 0.079 0.072 0.065 0.059 0.053 0.047 0.042 0.038 0.033 0.029 0.026 0.022 0.019 0.016

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

2.041 2.038 2.036 2.033 2.031 2.028 2.026 2.024 2.022 2.021 2.019 2.017 2.016 2.014 2.013 2.012 2.010 2.009

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050

1.9953 0 1.9947 0 1.9942 0 1.9937 0 1.9932 0 1.9927 0 1.9922 0 1.9918 0 1.9913 0 1.9909 0 1.9905 0 1.9901 0 1.9897 0 1.9893 0 1.9890 0 1.9886 0 1.9883 0 1.9879 0 (continued)

k

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Table 8.16 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.140 2.134 2.129 2.118 2.108 2.099 2.090 2.083 2.076 2.070 2.065 2.060 2.056 2.052 2.048 2.045

0.014 0.012 0.010 0.006 0.003 0.002 0 0 0 0 0 0 0 0 0 0

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.008 2.007 2.006 2.005 2.004 2.003 2.002 2.001 2.001 2 1.999 1.998 1.998 1.997 1.996 1.996

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.9876 1.9873 1.9870 1.9867 1.9864 1.9861 1.9859 1.9856 1.9853 1.9851 1.9848 1.9846 1.9844 1.9842 1.9839

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8.2.7

a-Si:H

Data from R. W. Collins and K. Vedam [12]. The optical data have been extracted from a hydrogenated amorphous silicon (a-Si:H) layer prepared by conventional plasma-enhanced chemical vapor deposition (Fig. 8.7, Tables 8.17 and 8.18).

Fig. 8.7 Dielectric function and absorption coefficient of a-Si:H at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

8 Inorganic Semiconductors and Passivation Layers

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Table 8.17 Tauc-Lorentz parameters of (8.1) and (8.2) for a-Si:H Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

3.497 × 10−6 2.364 × 10−4 0.034 4.268 × 10−3 179.062 116.664

0.254 0.715 0.108 0.406 2.351 1.488

0.806 1.341 1.652 1.784 3.458 3.691

0.432 0.791 1.294 1.211 1.637 2.555

−0.411 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

Table 8.18 Optical constants of a-Si:H. The optical data of Collins et al. are shown λ (nm) 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

n 3.515 3.664 3.810 3.952 4.088 4.217 4.339 4.452 4.555 4.650 4.734 4.808 4.873 4.928 4.975 5.013 5.044 5.067 5.084 5.096 5.102 5.102 5.087 5.062 5.030 4.992 4.950 4.906 4.861 4.815 4.769 4.724 4.679 4.635

k 3.703 3.664 3.615 3.555 3.485 3.406 3.318 3.224 3.123 3.017 2.908 2.797 2.684 2.571 2.459 2.349 2.240 2.135 2.032 1.933 1.838 1.659 1.496 1.347 1.213 1.092 0.982 0.884 0.795 0.715 0.642 0.577 0.518 0.464

λ (nm) 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

n 4.593 4.551 4.510 4.471 4.433 4.396 4.360 4.326 4.293 4.260 4.229 4.199 4.170 4.142 4.115 4.089 4.064 4.040 4.017 3.995 3.973 3.953 3.934 3.915 3.898 3.881 3.866 3.853 3.840 3.828 3.817 3.806 3.796 3.787

k 0.415 0.371 0.329 0.286 0.246 0.212 0.178 0.15 0.125 0.103 8.51 × 6.99 × 5.64 × 4.57 × 3.64 × 2.79 × 1.96 × 1.32 × 8.22 × 5.26 × 3.33 × 2.10 × 1.37 × 9.14 × 6.14 × 4.20 × 2.90 × 2.03 × 1.43 × 1.01 × 7.26 × 5.39 × 3.95 × 3.01 ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−5 10−5 10−5 10−5

λ (nm) 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

n 3.756 3.747 3.739 3.731 3.724 3.717 3.710 3.704 3.698 3.692 3.686 3.681 3.675 3.670 3.665 3.661 3.656 3.652 3.647 3.643 3.639 3.635 3.632 3.628 3.624 3.621 3.618 3.615 3.611 3.608 3.606 3.603 3.600

k 2.40 1.88 1.53 1.27 1.11 9.84 8.82 8.02 7.47 6.96 6.57 6.21 5.88 5.57 5.27 5.00 4.76 4.50 4.31 4.06 3.84 3.66 3.46 3.25 3.08 2.88 2.74 2.57 2.42 2.27 2.09 1.91 1.77

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−5 10−5 10−5 10−5 10−5 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6

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A. Nakane et al.

a-Si:H Layers

Data from S. Kageyama, M. Akagawa and H. Fujiwara [13] (see also Fig. 9.11a in Vol. 1). The optical data have been extracted from various a-Si:H layers prepared by plasma-enhanced chemical vapor deposition at different substrate temperatures (Ts = 80–280 °C). The dielectric functions modeled assuming a single Tauc-Lorentz peak are summarized. In the modeling, the effect of the tail-state absorption is neglected (Tables 8.19, 8.20, 8.21, 8.22, 8.23 and 8.24).

Fig. 8.8 Dielectric functions of a-Si:H layers calculated from the Tauc-Lorentz parameters reported by Kageyama et al. The results for various a-Si:H layers prepared at different substrate temperature (Ts) are shown

Table 8.19 Tauc-Lorentz parameters of (8.1) and (8.2) for the a-Si:H dielectric function in Fig. 8.8, reported by Kageyama et al. Ts (°C)

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

80 130 180 230 280

199.37 207.94 211.90 214.05 217.98

2.33 2.33 2.33 2.33 2.33

3.673 3.670 3.656 3.649 3.637

1.744 1.717 1.688 1.659 1.627

0.920 0.597 0.440 0.309 0.073

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Table 8.20 Optical constants of a-Si:H (Ts = 80 °C) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.461 3.590 3.716 3.838 3.954 4.065 4.169 4.266 4.355 4.436 4.508 4.573 4.629 4.677 4.718 4.752 4.779 4.800 4.815 4.825 4.831 4.830 4.816 4.792 4.761 4.725 4.685 4.642 4.598 4.552 4.507 4.462 4.417 4.373

3.223 3.184 3.136 3.080 3.016 2.944 2.866 2.781 2.692 2.599 2.503 2.406 2.307 2.207 2.109 2.011 1.915 1.822 1.731 1.642 1.557 1.396 1.249 1.114 0.992 0.881 0.782 0.692 0.611 0.539 0.473 0.415 0.362 0.314

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

4.330 4.288 4.247 4.207 4.169 4.131 4.095 4.060 4.027 3.995 3.964 3.934 3.906 3.879 3.854 3.830 3.807 3.787 3.768 3.751 3.736 3.722 3.709 3.696 3.684 3.673 3.663 3.653 3.644 3.635 3.627 3.619 3.611 3.604

0.272 0.234 0.200 0.169 0.142 0.118 0.097 0.078 0.062 0.048 0.036 0.026 0.018 0.011 0.006 0.003 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.597 3.590 3.584 3.578 3.572 3.566 3.561 3.556 3.551 3.546 3.542 3.537 3.533 3.529 3.525 3.521 3.517 3.514 3.510 3.507 3.504 3.501 3.498 3.495 3.492 3.489 3.487 3.484 3.482 3.479 3.477 3.474 3.472

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.21 Optical constants of a-Si:H (Ts = 130 °C) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.523 3.656 3.786 3.912 4.033 4.148 4.256 4.356 4.449 4.533 4.609 4.676 4.735 4.786 4.829 4.865 4.894 4.916 4.933 4.945 4.951 4.952 4.939 4.916 4.885 4.849 4.808 4.765 4.720 4.674 4.628 4.581 4.536 4.491

3.370 3.330 3.281 3.224 3.158 3.084 3.004 2.917 2.825 2.730 2.631 2.530 2.428 2.325 2.223 2.122 2.023 1.926 1.831 1.740 1.651 1.484 1.330 1.190 1.062 0.947 0.843 0.748 0.664 0.587 0.518 0.456 0.400 0.350

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

4.447 4.403 4.361 4.321 4.281 4.242 4.205 4.169 4.135 4.101 4.069 4.038 4.009 3.981 3.954 3.928 3.904 3.882 3.861 3.842 3.825 3.810 3.795 3.781 3.769 3.757 3.746 3.735 3.725 3.716 3.706 3.698 3.690 3.682

0.305 0.264 0.227 0.195 0.165 0.139 0.116 0.095 0.077 0.061 0.048 0.036 0.026 0.018 0.012 0.007 0.003 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.674 3.667 3.661 3.654 3.648 3.642 3.636 3.631 3.625 3.620 3.615 3.611 3.606 3.602 3.597 3.593 3.589 3.586 3.582 3.578 3.575 3.572 3.568 3.565 3.562 3.559 3.556 3.554 3.551 3.548 3.546 3.543 3.541

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.22 Optical constants of a-Si:H (Ts = 180 °C) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.536 3.672 3.805 3.934 4.057 4.176 4.287 4.391 4.487 4.575 4.655 4.726 4.789 4.843 4.890 4.929 4.961 4.987 5.006 5.020 5.029 5.034 5.025 5.004 4.975 4.940 4.901 4.858 4.814 4.768 4.722 4.676 4.630 4.585

3.465 3.427 3.380 3.324 3.260 3.187 3.108 3.022 2.931 2.835 2.736 2.634 2.531 2.428 2.324 2.222 2.121 2.022 1.925 1.831 1.740 1.569 1.410 1.265 1.133 1.013 0.904 0.806 0.717 0.637 0.565 0.500 0.441 0.388

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

4.540 4.497 4.454 4.413 4.373 4.334 4.296 4.260 4.224 4.190 4.157 4.126 4.095 4.066 4.038 4.012 3.986 3.962 3.940 3.919 3.900 3.883 3.867 3.853 3.839 3.826 3.814 3.803 3.792 3.782 3.773 3.763 3.755 3.746

0.340 0.297 0.258 0.223 0.191 0.163 0.137 0.115 0.095 0.077 0.062 0.048 0.037 0.027 0.019 0.012 0.007 0.004 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.739 3.731 3.724 3.717 3.710 3.704 3.698 3.692 3.686 3.681 3.676 3.671 3.666 3.662 3.657 3.653 3.649 3.645 3.641 3.637 3.633 3.630 3.627 3.623 3.620 3.617 3.614 3.611 3.608 3.606 3.603 3.600 3.598

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.23 Optical constants of a-Si:H (Ts = 230 °C) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.553 3.690 3.825 3.957 4.083 4.204 4.318 4.425 4.524 4.615 4.698 4.772 4.837 4.894 4.943 4.985 5.019 5.047 5.068 5.084 5.095 5.103 5.096 5.077 5.050 5.017 4.978 4.937 4.893 4.848 4.802 4.756 4.710 4.665

3.548 3.511 3.465 3.410 3.346 3.274 3.195 3.109 3.018 2.922 2.823 2.721 2.617 2.512 2.408 2.304 2.201 2.101 2.003 1.907 1.814 1.639 1.477 1.328 1.193 1.069 0.958 0.857 0.765 0.682 0.607 0.540 0.478 0.423

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

4.621 4.577 4.535 4.493 4.453 4.414 4.375 4.339 4.303 4.269 4.235 4.203 4.172 4.143 4.114 4.087 4.060 4.036 4.012 3.990 3.969 3.950 3.933 3.917 3.902 3.889 3.876 3.864 3.853 3.842 3.832 3.822 3.813 3.804

0.373 0.328 0.287 0.250 0.216 0.186 0.159 0.135 0.113 0.094 0.077 0.062 0.049 0.037 0.028 0.020 0.013 0.008 0.004 0.002 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.796 3.788 3.780 3.773 3.766 3.760 3.753 3.747 3.741 3.736 3.730 3.725 3.720 3.715 3.710 3.706 3.702 3.697 3.693 3.689 3.686 3.682 3.678 3.675 3.672 3.668 3.665 3.662 3.659 3.656 3.654 3.651 3.648

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.24 Optical constants of a-Si:H (Ts = 280 °C) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.567 3.708 3.845 3.980 4.109 4.233 4.351 4.462 4.565 4.660 4.746 4.824 4.893 4.953 5.006 5.051 5.088 5.119 5.143 5.162 5.175 5.187 5.183 5.167 5.142 5.110 5.073 5.033 4.989 4.945 4.899 4.853 4.808 4.762

3.657 3.622 3.577 3.523 3.460 3.389 3.311 3.226 3.135 3.039 2.939 2.836 2.731 2.625 2.519 2.413 2.309 2.207 2.106 2.008 1.913 1.733 1.566 1.412 1.272 1.144 1.028 0.922 0.827 0.740 0.662 0.591 0.527 0.468

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

4.718 4.674 4.631 4.589 4.548 4.509 4.470 4.433 4.396 4.361 4.327 4.295 4.263 4.232 4.203 4.175 4.148 4.122 4.097 4.073 4.051 4.030 4.011 3.993 3.977 3.962 3.948 3.935 3.923 3.911 3.900 3.890 3.880 3.871

0.415 0.367 0.324 0.284 0.248 0.216 0.187 0.160 0.137 0.115 0.096 0.079 0.064 0.051 0.040 0.030 0.022 0.015 0.010 0.006 0.003 0.001 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.862 3.854 3.846 3.838 3.830 3.823 3.817 3.810 3.804 3.798 3.792 3.787 3.781 3.776 3.771 3.766 3.762 3.757 3.753 3.749 3.745 3.741 3.737 3.734 3.730 3.727 3.723 3.720 3.717 3.714 3.711 3.708 3.705

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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8.2.9

a-SiC:H

The dielectric functions of hydrogenated amorphous silicon carbide (a-Si1−xCx:H) alloys (x = 0.1–0.3) were calculated from the model parameters shown in Fig. 9.16 of Vol. 1 (see also M. Sato, S. W. King, W. A. Lanford, P. Henry, T. Fujiseki, and H. Fujiwara [14]). The original optical data were extracted from a-SiC:H layers prepared by plasma-enhanced chemical vapor deposition at 180 °C using different SiH4/CH4 gas flow ratios. The dielectric functions modeled assuming a single Tauc-Lorentz peak are summarized. In the modeling, the effect of the tail-state absorption is neglected (Tables 8.25, 8.26, 8.27 and 8.28).

Fig. 8.9 Dielectric functions of a-Si1−xCx:H layers calculated from the Tauc-Lorentz parameters reported by Sato et al. The results for various a-Si1−xCx:H layers with different carbon content x are shown

Table 8.25 Tauc-Lorentz parameters for the a-Si1−xCx:H dielectric functions in Fig. 8.9, reported by Sato et al. Alloy content x

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

x x x x

213.848 192.668 182.601 174.651

2.309 2.602 3.082 3.282

3.650 3.659 3.667 3.676

1.674 1.972 2.182 2.392

0.059 1.179 1.359 1.539

= = = =

0.0 0.1 0.2 0.3

8 Inorganic Semiconductors and Passivation Layers

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Table 8.26 Optical constants of a-Si1−xCx:H (x = 0.1) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.210 3.306 3.398 3.487 3.571 3.651 3.725 3.793 3.856 3.913 3.964 4.009 4.049 4.082 4.111 4.134 4.152 4.166 4.175 4.181 4.183 4.178 4.163 4.140 4.110 4.075 4.037 3.996 3.954 3.911 3.867 3.824 3.781 3.738

2.497 2.457 2.410 2.358 2.301 2.239 2.173 2.104 2.031 1.957 1.880 1.803 1.725 1.647 1.569 1.492 1.417 1.343 1.271 1.201 1.134 1.005 0.887 0.778 0.679 0.589 0.509 0.436 0.371 0.313 0.262 0.217 0.177 0.142

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.696 3.656 3.617 3.579 3.542 3.507 3.475 3.444 3.415 3.389 3.367 3.348 3.330 3.314 3.299 3.285 3.272 3.260 3.249 3.238 3.228 3.219 3.210 3.202 3.194 3.186 3.179 3.172 3.166 3.160 3.154 3.149 3.143 3.138

0.112 0.086 0.064 0.045 0.031 0.019 0.010 0.004 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.133 3.129 3.124 3.120 3.116 3.112 3.108 3.104 3.101 3.097 3.094 3.091 3.088 3.085 3.082 3.079 3.077 3.074 3.072 3.069 3.067 3.065 3.063 3.061 3.058 3.057 3.055 3.053 3.051 3.049 3.047 3.046 3.044

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.27 Optical constants of a-Si1−xCx:H (x = 0.2) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.986 3.050 3.111 3.169 3.223 3.273 3.320 3.362 3.401 3.435 3.465 3.492 3.514 3.533 3.549 3.561 3.569 3.575 3.578 3.578 3.576 3.565 3.546 3.522 3.492 3.459 3.422 3.384 3.344 3.304 3.263 3.222 3.182 3.143

1.814 1.773 1.729 1.682 1.632 1.580 1.526 1.470 1.413 1.355 1.296 1.238 1.179 1.120 1.063 1.006 0.950 0.895 0.842 0.790 0.739 0.644 0.556 0.475 0.401 0.334 0.275 0.222 0.176 0.136 0.101 0.072 0.049 0.030

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.106 3.071 3.038 3.010 2.986 2.965 2.947 2.930 2.915 2.901 2.889 2.877 2.866 2.856 2.846 2.838 2.829 2.822 2.814 2.807 2.801 2.795 2.789 2.783 2.778 2.773 2.768 2.764 2.760 2.755 2.751 2.748 2.744 2.741

0.016 0.007 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.737 2.734 2.731 2.728 2.725 2.723 2.720 2.718 2.715 2.713 2.711 2.708 2.706 2.704 2.702 2.700 2.699 2.697 2.695 2.693 2.692 2.690 2.689 2.687 2.686 2.684 2.683 2.682 2.681 2.679 2.678 2.677 2.676

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.28 Optical constants of a-Si1−xCx:H (x = 0.3) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.822 2.871 2.916 2.958 2.997 3.032 3.064 3.093 3.117 3.139 3.157 3.172 3.183 3.192 3.197 3.200 3.200 3.198 3.194 3.187 3.179 3.156 3.128 3.096 3.059 3.020 2.980 2.939 2.897 2.857 2.818 2.782 2.750 2.725

1.391 1.351 1.308 1.263 1.216 1.168 1.119 1.069 1.018 0.967 0.916 0.865 0.815 0.765 0.717 0.669 0.622 0.577 0.534 0.491 0.451 0.375 0.306 0.244 0.190 0.143 0.103 0.070 0.043 0.023 0.010 0.002 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.703 2.685 2.668 2.653 2.640 2.627 2.616 2.606 2.596 2.587 2.579 2.571 2.564 2.557 2.551 2.545 2.539 2.534 2.529 2.524 2.520 2.515 2.511 2.508 2.504 2.500 2.497 2.494 2.491 2.488 2.485 2.483 2.480 2.478

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.475 2.473 2.471 2.469 2.467 2.465 2.463 2.461 2.460 2.458 2.456 2.455 2.453 2.452 2.451 2.449 2.448 2.447 2.445 2.444 2.443 2.442 2.441 2.440 2.439 2.438 2.437 2.436 2.435 2.434 2.433 2.432 2.432

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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8.2.10 a-SiO:H The dielectric functions of hydrogenated amorphous silicon oxide (a-Si1−xOx:H) alloys (x = 0.1–0.3) were calculated from the model parameters shown in Fig. 9.16 of Vol. 1 (see also M. Sato, S. W. King, W. A. Lanford, P. Henry, T. Fujiseki, and H. Fujiwara [14]). The original optical data were extracted from a-SiO:H layers prepared by plasma-enhanced chemical vapor deposition at 180 °C using different SiH4/CO2 gas mixtures. The dielectric functions modeled assuming a single Tauc-Lorentz peak are summarized. In the modeling, the effect of the tail-state absorption is neglected (Tables 8.29, 8.30, 8.31 and 8.32).

Fig. 8.10 Dielectric functions of a-Si1−xOx:H layers calculated from the Tauc-Lorentz parameters reported by Sato et al. The results for various a-Si1−xOx:H layers with different oxygen content x are shown

Table 8.29 Tauc-Lorentz parameters for the a-Si1−xOx:H dielectric functions in Fig. 8.10, reported by Sato et al. Alloy content x

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

x x x x

212.128 190.950 169.772 148.594

2.313 2.435 2.790 3.376

3.649 3.691 3.733 3.746

1.670 1.873 2.076 2.280

0.013 0.708 1.273 1.479

= = = =

0.0 0.1 0.2 0.3

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Table 8.30 Optical constants of a-Si1−xOx:H (x = 0.1) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.298 3.410 3.518 3.621 3.720 3.812 3.899 3.979 4.051 4.117 4.175 4.226 4.270 4.307 4.338 4.363 4.383 4.397 4.406 4.411 4.412 4.404 4.386 4.359 4.325 4.287 4.246 4.203 4.158 4.113 4.068 4.023 3.979 3.935

2.839 2.796 2.745 2.687 2.623 2.553 2.477 2.398 2.314 2.228 2.140 2.051 1.961 1.872 1.783 1.696 1.610 1.527 1.446 1.367 1.292 1.149 1.018 0.899 0.792 0.695 0.607 0.529 0.458 0.395 0.339 0.289 0.244 0.205

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.893 3.852 3.811 3.773 3.735 3.699 3.664 3.631 3.600 3.570 3.542 3.516 3.492 3.471 3.452 3.435 3.419 3.404 3.391 3.378 3.366 3.355 3.344 3.334 3.325 3.316 3.308 3.300 3.292 3.285 3.278 3.272 3.265 3.260

0.170 0.139 0.112 0.089 0.069 0.052 0.038 0.026 0.016 0.009 0.004 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.254 3.248 3.243 3.238 3.233 3.229 3.224 3.220 3.216 3.212 3.208 3.204 3.201 3.197 3.194 3.191 3.188 3.185 3.182 3.179 3.176 3.174 3.171 3.169 3.167 3.164 3.162 3.160 3.158 3.156 3.154 3.152 3.150

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.31 Optical constants of a-Si1−xOx:H (x = 0.2) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.057 3.135 3.209 3.279 3.345 3.406 3.461 3.512 3.558 3.598 3.634 3.664 3.690 3.712 3.729 3.742 3.751 3.757 3.759 3.759 3.756 3.743 3.722 3.695 3.664 3.629 3.591 3.552 3.512 3.472 3.432 3.392 3.352 3.314

2.072 2.028 1.979 1.926 1.870 1.810 1.748 1.684 1.618 1.550 1.483 1.415 1.347 1.280 1.214 1.149 1.086 1.024 0.965 0.907 0.851 0.746 0.649 0.562 0.482 0.411 0.347 0.290 0.239 0.195 0.156 0.122 0.094 0.069

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.277 3.241 3.206 3.174 3.143 3.115 3.090 3.069 3.050 3.034 3.018 3.004 2.991 2.979 2.968 2.958 2.948 2.939 2.930 2.922 2.914 2.907 2.901 2.894 2.888 2.882 2.877 2.871 2.866 2.862 2.857 2.853 2.849 2.845

0.049 0.033 0.020 0.010 0.004 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.841 2.837 2.834 2.830 2.827 2.824 2.821 2.818 2.815 2.813 2.810 2.808 2.805 2.803 2.801 2.798 2.796 2.794 2.792 2.790 2.789 2.787 2.785 2.783 2.782 2.780 2.779 2.777 2.776 2.774 2.773 2.772 2.770

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 8.32 Optical constants of a-Si1−xOx:H (x = 0.3) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.742 2.790 2.834 2.876 2.914 2.949 2.981 3.010 3.035 3.057 3.076 3.092 3.105 3.115 3.122 3.127 3.130 3.130 3.128 3.125 3.119 3.104 3.083 3.058 3.029 2.997 2.964 2.929 2.894 2.859 2.824 2.789 2.756 2.725

1.396 1.357 1.316 1.274 1.230 1.184 1.138 1.090 1.042 0.994 0.946 0.898 0.851 0.804 0.758 0.713 0.669 0.626 0.585 0.545 0.506 0.433 0.365 0.304 0.250 0.201 0.158 0.120 0.089 0.062 0.040 0.024 0.012 0.004

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.697 2.674 2.654 2.637 2.621 2.608 2.595 2.584 2.573 2.564 2.555 2.546 2.539 2.531 2.524 2.518 2.512 2.507 2.501 2.496 2.491 2.487 2.483 2.479 2.475 2.471 2.468 2.464 2.461 2.458 2.455 2.452 2.450 2.447

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.445 2.442 2.440 2.438 2.436 2.434 2.432 2.430 2.428 2.427 2.425 2.423 2.422 2.420 2.419 2.417 2.416 2.415 2.414 2.412 2.411 2.410 2.409 2.408 2.407 2.406 2.405 2.404 2.403 2.402 2.401 2.400 2.399

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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8.2.11 μc-Si:H Data from T. Yuguchi, Y. Kanie, N. Matsuki and H. Fujiwara [15]. The optical data have been extracted from microcrystalline Si (μc-Si:H) layers prepared by plasma-enhanced chemical vapor deposition at 190 °C using different SiH4/H2 gas flow ratios. The dielectric function of μc-Si:H is modeled by combining the Tauc-Lorentz model with the harmonic oscillator (HO) model   2  2 2 εHO ðEÞ = ACE0 ̸ E0 − E + iCE + 0.25C . The variation of the model parameters with a film structure is further expressed by using a μc-Si:H structural factor κ. Depending on the μc-Si:H volume fraction, the κ value changes from zero (amorphous phase) to one (complete μc-Si:H phase). In this model, however, the optical properties in a weak absorption region (α < 103 cm−1) are not modeled accurately (Tables 8.33, 8.34, 8.35 and 8.36).

Fig. 8.11 Dielectric functions of a-Si:H (κ = 0) and μc-Si:H (κ > 0) calculated from the Tauc-Lorentz and harmonic oscillator models with the parameters reported by Yuguchi et al. The κ is a structural factor of μc-Si:H. The Tauc-Lorentz parameters of a-Si:H (κ = 0) are A = 224.9 eV, C = 2.321 eV, E0 = 3.666 eV, Eg = 1.733 eV and ε1(∞) = 1

Table 8.33 Tauc-Lorentz (TL) and harmonic oscillator (HO) parameters for the μc-Si:H (κ = 0.5) dielectric function in Fig. 8.11, reported by Yuguchi et al. Model

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 HO peak

137.065 202.831 8.375

1.659 0.493 0.590

3.875 3.360 4.250

1.766 3.052 –

1 0 –

8 Inorganic Semiconductors and Passivation Layers

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Table 8.34 Tauc-Lorentz (TL) and harmonic oscillator (HO) parameters for the μc-Si:H (κ = 1.0) dielectric function in Fig. 8.11, reported by Yuguchi et al. Model

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 HO peak

135.1 203.9 16.750

1.629 0.476 0.691

3.875 3.360 4.250

2.033 3.096 –

1 0 –

Table 8.35 Optical constants of μc-Si:H (κ = 0.5) calculated by the Tauc-Lorentz and harmonic oscillator models λ (nm) 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

n 4.271 4.429 4.558 4.673 4.780 4.880 4.974 5.062 5.143 5.220 5.293 5.362 5.420 5.457 5.465 5.440 5.389 5.322 5.250 5.178 5.111 4.997 4.902 4.815 4.735 4.660 4.590 4.525 4.464 4.407 4.354 4.303 4.256 4.212

k 3.868 3.690 3.530 3.384 3.244 3.106 2.969 2.831 2.692 2.552 2.406 2.251 2.081 1.898 1.709 1.527 1.364 1.226 1.113 1.019 0.942 0.818 0.713 0.622 0.542 0.474 0.414 0.362 0.317 0.277 0.242 0.211 0.184 0.160

λ (nm) 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

n 4.171 4.131 4.094 4.059 4.026 3.995 3.966 3.938 3.911 3.886 3.862 3.840 3.819 3.799 3.780 3.763 3.746 3.731 3.718 3.705 3.693 3.681 3.671 3.661 3.651 3.642 3.634 3.625 3.618 3.610 3.603 3.597 3.590 3.584

k 0.138 0.120 0.103 8.86 × 7.58 × 6.46 × 5.48 × 4.63 × 3.90 × 3.27 × 2.75 × 2.32 × 1.97 × 1.70 × 1.50 × 1.36 × 1.29 × 1.27 × 1.24 × 1.21 × 1.19 × 1.17 × 1.14 × 1.12 × 1.10 × 1.08 × 1.06 × 1.04 × 1.03 × 1.01 × 9.92 × 9.76 × 9.61 × 9.45 ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3

λ (nm) 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

n 3.578 3.573 3.567 3.562 3.557 3.552 3.548 3.543 3.539 3.535 3.531 3.527 3.523 3.520 3.516 3.513 3.510 3.507 3.503 3.501 3.498 3.495 3.492 3.490 3.487 3.485 3.482 3.480 3.478 3.476 3.474 3.472 3.470

k 9.31 9.17 9.04 8.90 8.78 8.65 8.53 8.42 8.31 8.19 8.09 7.98 7.89 7.79 7.69 7.60 7.51 7.42 7.33 7.25 7.17 7.08 7.01 6.93 6.86 6.78 6.71 6.64 6.57 6.51 6.44 6.38 6.31

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

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Table 8.36 Optical constants of μc-Si:H (κ = 1.0) calculated by the Tauc-Lorentz and harmonic oscillator models λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

4.680 4.831 4.930 4.999 5.053 5.099 5.140 5.178 5.214 5.250 5.285 5.319 5.345 5.355 5.338 5.292 5.225 5.146 5.066 4.990 4.921 4.807 4.707 4.615 4.532 4.454 4.383 4.316 4.255 4.197 4.144 4.094 4.048 4.005

3.804 3.538 3.299 3.089 2.903 2.735 2.579 2.431 2.289 2.151 2.011 1.866 1.709 1.541 1.369 1.206 1.065 0.948 0.854 0.779 0.718 0.615 0.526 0.451 0.386 0.332 0.285 0.245 0.210 0.181 0.156 0.135 0.116 0.101

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.965 3.927 3.892 3.860 3.829 3.801 3.775 3.751 3.730 3.710 3.692 3.676 3.660 3.645 3.632 3.619 3.607 3.596 3.585 3.575 3.566 3.556 3.548 3.540 3.532 3.525 3.517 3.511 3.504 3.498 3.492 3.486 3.481 3.476

8.79 7.71 6.82 6.10 5.53 5.11 4.81 4.62 4.49 4.36 4.25 4.14 4.03 3.93 3.84 3.75 3.66 3.58 3.50 3.43 3.36 3.29 3.23 3.17 3.11 3.05 2.99 2.94 2.89 2.84 2.79 2.75 2.70 2.66

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.471 3.466 3.461 3.457 3.453 3.449 3.445 3.441 3.437 3.434 3.430 3.427 3.424 3.421 3.418 3.415 3.412 3.409 3.407 3.404 3.402 3.399 3.397 3.395 3.393 3.391 3.389 3.387 3.385 3.383 3.381 3.379 3.377

2.62 2.58 2.54 2.51 2.47 2.43 2.40 2.37 2.34 2.30 2.27 2.24 2.22 2.19 2.16 2.13 2.11 2.08 2.06 2.04 2.01 1.99 1.97 1.95 1.93 1.90 1.88 1.86 1.85 1.83 1.81 1.79 1.77

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

8.2.12 AlAs Data from C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs and J. A. Woollam [16]. The optical data of an AlAs epitaxial layer formed on a GaAs substrate are shown (Fig. 8.12, Tables 8.37 and 8.38).

8 Inorganic Semiconductors and Passivation Layers

357

Fig. 8.12 Dielectric function and absorption coefficient of AlAs at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.37 Tauc-Lorentz parameters of (8.1) and (8.2) for AlAs Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j

0.599 0.246 2.871 3.229 135.050 278.284 181.787 115.203 165.705 126.095

0.177 0.321 2.198 0.173 0.160 2.431 0.242 0.408 0.619 0.283

2.152 2.174 2.179 2.936 2.953 3.109 3.893 4.063 4.703 4.953

2.151 2.129 2.178 2.691 2.925 2.976 3.492 3.304 3.351 4.454

0.378 0 0 0 0 0 0 0 0 0

= = = = = = = = = =

1 2 3 4 5 6 7 8 9 10

Table 8.38 Optical constants of AlAs. The optical data reported by Herzinger et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340

4.459 4.714 4.926 5.157 5.331 5.265 5.046 4.829 4.658

2.307 2.228 2.059 1.836 1.435 0.986 0.687 0.532 0.446

540 550 560 570 580 590 600 610 620

3.238 3.220 3.204 3.188 3.173 3.160 3.148 3.136 3.125

1.44 9.69 5.10 1.22 2.71 0 0 0 0

λ (nm) × × × × ×

10−3 10−4 10−4 10−4 10−6

880 890 900 910 920 930 940 950 960

n

k

2.978 0 2.975 0 2.972 0 2.969 0 2.967 0 2.964 0 2.962 0 2.959 0 2.957 0 (continued)

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Table 8.38 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

4.523 4.412 4.319 4.240 4.172 4.113 4.059 4.005 3.956 3.912 3.873 3.837 3.777 3.715 3.628 3.561 3.506 3.460 3.421 3.386 3.355 3.327 3.302 3.279 3.258

0.388 0.344 0.310 0.281 0.256 0.232 0.206 0.183 0.166 0.150 0.135 0.121 9.18 × 3.58 × 1.52 × 8.58 × 6.43 × 5.63 × 5.07 × 4.52 × 3.98 × 3.45 × 2.93 × 2.42 × 1.93 ×

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.115 3.105 3.096 3.088 3.080 3.072 3.065 3.058 3.051 3.045 3.040 3.034 3.029 3.024 3.019 3.014 3.010 3.006 3.002 2.998 2.994 2.990 2.987 2.984 2.981

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.955 2.953 2.951 2.949 2.947 2.945 2.943 2.941 2.940 2.938 2.937 2.935 2.934 2.932 2.931 2.929 2.928 2.927 2.925 2.924 2.923 2.922 2.921 2.920

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

8.2.13 GaAs To express the dielectric function of a GaAs single crystal, two separate data sets are used depending on the energy region: (i) Data of G. E. Jellison, Jr. [1] for E ≥ 2.72 eV, (ii) Unpublished data of C. M. Herzinger [2] for E < 2.72 eV. The result of [2] above was determined from a multiple data set analysis. The data sets include ellipsometry results [1, 2], transmittance results [17], and compiled values from a handbook edited by E. D. Palik [3] originally from ellipsometry results [18] and from prism and reflectance results [19]. The analysis procedure is described in the Ge section in this chapter (Fig. 8.13, Tables 8.39 and 8.40).

8 Inorganic Semiconductors and Passivation Layers

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Fig. 8.13 Dielectric function and absorption coefficient of GaAs at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.39 Tauc-Lorentz parameters of (8.1) and (8.2) for GaAs Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j j j

8.732 × 10−3 39.387 3.326 13.956 11.274 38.219 94.522 4.161 22.799 18.058 16.031 967.771

0.038 0.108 0.044 1.054 1.004 0.170 1.040 0.229 1.199 0.662 0.502 0.599

1.354 1.405 1.413 1.744 2.286 2.917 3.128 3.134 3.885 4.549 4.870 5.084

1.267 1.394 1.350 1.360 1.638 2.382 2.076 1.561 2.172 1.422 1.400 5.103

0.544 0 0 0 0 0 0 0 0 0 0 0

= = = = = = = = = = = =

1 2 3 4 5 6 7 8 9 10 11 12

Table 8.40 Optical constants of GaAs. The optical data, obtained by G. E. Jellison and C. M. Herzinger, are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335

3.817 3.735 3.675 3.633 3.598 3.579 3.564 3.564

1.947 1.908 1.887 1.876 1.874 1.879 1.890 1.901

540 550 560 570 580 590 600 610

4.083 4.044 4.009 3.978 3.950 3.924 3.901 3.880

0.298 0.282 0.268 0.256 0.245 0.235 0.226 0.217

λ (nm) 880 890 900 910 920 930 940 950

n

k

3.636 3.619 3.598 3.582 3.570 3.559 3.549 3.541

2.48 × 10−2 7.53 × 10−3 1.43 × 10−3 2.67 × 10−4 8.03 × 10−5 2.89 × 10−5 9.81 × 10−6 3.02 × 10−6 (continued)

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Table 8.40 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.566 3.576 3.592 3.612 3.642 3.682 3.727 3.786 3.856 3.962 4.124 4.323 4.459 4.557 4.755 5.152 5.041 4.858 4.688 4.557 4.452 4.367 4.294 4.232 4.176 4.127

1.919 1.939 1.961 1.990 2.019 2.050 2.087 2.125 2.176 2.232 2.262 2.209 2.081 1.902 1.887 1.438 0.990 0.755 0.631 0.541 0.480 0.434 0.396 0.365 0.339 0.317

620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.861 3.843 3.827 3.812 3.799 3.787 3.776 3.766 3.755 3.743 3.731 3.719 3.709 3.699 3.690 3.682 3.675 3.668 3.661 3.655 3.650 3.645 3.642 3.640 3.642 3.646

0.209 0.201 0.194 0.187 0.180 0.173 0.166 0.157 0.148 0.139 0.131 0.125 0.120 0.115 0.111 0.106 0.102 9.72 × 9.28 × 8.84 × 8.40 × 7.97 × 7.53 × 7.09 × 6.39 × 4.84 ×

960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.533 3.526 3.519 3.513 3.507 3.501 3.496 3.491 3.486 3.481 3.477 3.472 3.468 3.464 3.461 3.457 3.453 3.450 3.447 3.444 3.441 3.438 3.435 3.432 3.429

8.85 × 10−7 2.35 × 10−7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

8.2.14 InAs Data: unpublished results of C. M. Herzinger. These InAs optical constants are the result of a multiple data set analysis [2]. The data sets included original ellipsometric measurements for a 1-µm epitaxial layer on GaAs (D. Chow, Hughes Research Lab, Malibu CA) [2], other ellipsometric results [4], and transmittance results [20] compiled in a handbook edited by E. D. Palik [3]. The analysis procedure is described in the Ge section in this chapter (Fig. 8.14, Tables 8.41 and 8.42).

8 Inorganic Semiconductors and Passivation Layers

361

Fig. 8.14 Dielectric function and absorption coefficient of InAs at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)] Table 8.41 Tauc-Lorentz parameters of (8.1) and (8.2) for InAs Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j j j

0.002 1.293 2.175 4.766 3.647 9.262 18.212 82.887 34.752 3.791 250.267 36.029

0.050 0.062 0.079 0.236 1.030 1.640 0.293 0.314 2.500 0.844 4.091 0.576

0.329 0.373 0.392 0.416 0.623 0.829 2.497 2.718 3.144 3.917 4.256 4.458

0.169 0.320 0.359 0.393 0.622 0.471 1.630 2.355 0.720 1.583 4.150 2.117

0.336 0 0 0 0 0 0 0 0 0 0 0

= = = = = = = = = = = =

1 2 3 4 5 6 7 8 9 10 11 12

Table 8.42 Optical constants of InAs. The optical data obtained by C. M. Herzinger are shown λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345

3.530 3.429 3.342 3.269 3.208 3.159 3.120 3.091 3.068 3.052

1.959 1.857 1.790 1.748 1.724 1.711 1.706 1.708 1.713 1.720

λ (nm) 680 690 700 710 720 730 740 750 760 770

n

k

λ (nm)

n

k

3.845 3.829 3.814 3.800 3.787 3.775 3.763 3.753 3.743 3.734

0.498 0.487 0.476 0.467 0.457 0.449 0.441 0.434 0.427 0.421

1160 1170 1180 1190 1200 1220 1240 1260 1280 1300

3.601 3.600 3.600 3.599 3.598 3.597 3.596 3.595 3.595 3.594

0.296 0.294 0.292 0.291 0.289 0.285 0.281 0.278 0.274 0.271 (continued)

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Table 8.42 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670

3.041 3.033 3.029 3.029 3.031 3.037 3.046 3.059 3.075 3.096 3.120 3.182 3.262 3.370 3.553 3.780 3.921 3.987 4.056 4.208 4.419 4.492 4.448 4.385 4.322 4.262 4.206 4.155 4.109 4.068 4.032 4.000 3.971 3.945 3.922 3.900 3.880 3.862

1.730 1.742 1.756 1.772 1.789 1.808 1.830 1.853 1.877 1.903 1.929 1.985 2.045 2.115 2.176 2.123 1.990 1.889 1.848 1.820 1.666 1.395 1.186 1.045 0.940 0.859 0.795 0.744 0.702 0.668 0.640 0.615 0.593 0.574 0.556 0.539 0.525 0.511

780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150

3.725 3.717 3.709 3.702 3.695 3.689 3.683 3.677 3.672 3.667 3.662 3.658 3.653 3.650 3.646 3.643 3.639 3.636 3.633 3.631 3.628 3.626 3.623 3.621 3.619 3.618 3.616 3.614 3.613 3.611 3.610 3.608 3.607 3.606 3.605 3.604 3.603 3.602

0.414 0.409 0.403 0.398 0.393 0.389 0.384 0.380 0.376 0.372 0.369 0.365 0.362 0.358 0.355 0.352 0.349 0.346 0.343 0.340 0.338 0.335 0.332 0.330 0.327 0.325 0.322 0.320 0.318 0.315 0.313 0.311 0.309 0.307 0.305 0.302 0.300 0.298

1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1650 1700 1750 1800 1850 1900 1950 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3200 3400 3650 3875 4130

3.593 3.593 3.593 3.593 3.593 3.593 3.593 3.593 3.594 3.594 3.595 3.596 3.597 3.598 3.599 3.599 3.597 3.593 3.590 3.588 3.586 3.585 3.585 3.584 3.584 3.585 3.586 3.587 3.588 3.591 3.593 3.598 3.604 3.624 3.629 3.597 3.572 3.556

0.267 0.264 0.261 0.258 0.254 0.251 0.248 0.245 0.242 0.239 0.236 0.233 0.229 0.225 0.221 0.210 0.200 0.192 0.185 0.180 0.176 0.171 0.167 0.159 0.152 0.145 0.139 0.133 0.127 0.122 0.117 0.112 0.107 8.71 × 4.40 × 6.00 × 1.13 × 4.78 ×

10−2 10−2 10−3 10−3 10−4

8 Inorganic Semiconductors and Passivation Layers

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8.2.15 GaP Data: unpublished results of C. M. Herzinger. The optical data of a GaP single crystal was determined from a multiple data set analysis [2]. The data sets came from values compiled in a handbook edited by E. D. Palik [3] originally from ellipsometry results [4], from prism results [21, 22], and from transmittance results [23]. The analysis procedure is described in the Ge section in this chapter (Fig. 8.15, Tables 8.43 and 8.44).

Fig. 8.15 Dielectric function and absorption coefficient of GaP at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.43 Tauc-Lorentz parameters of (8.1) and (8.2) for GaP Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j

1.456 84.240 6.679 64.978 151.903 84.559 33.264 51.954 34.165 513.455

0.545 0.073 0.340 1.094 0.233 0.857 0.994 0.628 0.440 1.551

2.238 2.757 2.893 3.056 3.696 3.837 4.257 4.825 5.143 5.349

2.234 2.727 2.425 2.659 3.117 2.835 2.801 2.717 2.900 5.349

0.337 0 0 0 0 0 0 0 0 0

= = = = = = = = = =

1 2 3 4 5 6 7 8 9 10

364

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Table 8.44 Optical constants of GaP. The optical data, obtained by C. M. Herzinger, are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.846 3.858 3.892 3.952 4.048 4.237 4.671 5.272 5.555 5.460 5.247 5.052 4.892 4.759 4.645 4.545 4.457 4.380 4.312 4.253 4.200 4.111 4.039 3.981 3.931 3.889 3.794 3.727 3.673 3.627 3.587 3.553 3.522 3.494

2.049 2.088 2.142 2.214 2.317 2.478 2.604 2.352 1.736 1.200 0.881 0.699 0.579 0.492 0.426 0.375 0.335 0.303 0.277 0.255 0.236 0.202 0.172 0.142 0.108 5.01 × 1.40 × 7.95 × 4.78 × 3.07 × 2.14 × 1.56 × 1.10 × 6.75 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.469 3.445 3.424 3.405 3.387 3.371 3.355 3.341 3.328 3.315 3.304 3.293 3.283 3.273 3.264 3.255 3.247 3.240 3.232 3.225 3.219 3.212 3.206 3.201 3.195 3.190 3.185 3.180 3.176 3.172 3.167 3.163 3.159 3.156

2.63 × 10−4 2.13 × 10−5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.152 3.149 3.146 3.142 3.139 3.136 3.134 3.131 3.128 3.126 3.123 3.121 3.119 3.116 3.114 3.112 3.110 3.108 3.106 3.104 3.103 3.101 3.099 3.098 3.096 3.095 3.093 3.092 3.090 3.089 3.087 3.086 3.085

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−4

8 Inorganic Semiconductors and Passivation Layers

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8.2.16 InP Data from C. M. Herzinger, P. G. Snyder, B. Johs and J. A. Woollam [24]. The optical data of a single InP crystal are shown (Fig. 8.16, Tables 8.45 and 8.46).

Fig. 8.16 Dielectric function and absorption coefficient of InP at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.45 Tauc-Lorentz parameters of (8.1) and (8.2) for InP Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j j

0.058 25.819 0.011 22.949 7.629 14.442 84.556 48.192 10.794 114.471 121.715

0.078 0.062 0.549 0.274 0.654 0.834 0.349 1.588 1.088 0.571 1.686

1.318 1.339 1.342 1.407 1.749 1.989 3.143 3.249 4.174 4.707 5.584

1.200 1.304 1.161 1.326 1.279 1.740 2.574 1.622 1.601 3.320 4.830

1.355 0 0 0 0 0 0 0 0 0 0

= = = = = = = = = = =

1 2 3 4 5 6 7 8 9 10 11

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A. Nakane et al.

Table 8.46 Optical constants of InP. The optical data reported by Herzinger et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.257 3.212 3.180 3.157 3.143 3.135 3.133 3.138 3.151 3.171 3.200 3.239 3.288 3.350 3.444 3.595 3.775 3.950 4.135 4.321 4.446 4.450 4.343 4.237 4.144 4.066 4.000 3.943 3.893 3.847 3.807 3.770 3.736 3.706

1.698 1.691 1.693 1.699 1.711 1.727 1.748 1.774 1.805 1.840 1.879 1.922 1.970 2.028 2.100 2.157 2.157 2.115 2.042 1.899 1.686 1.278 1.032 0.876 0.769 0.690 0.628 0.578 0.535 0.499 0.469 0.443 0.420 0.401

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.679 3.655 3.633 3.613 3.595 3.578 3.563 3.550 3.538 3.527 3.517 3.508 3.499 3.492 3.485 3.479 3.473 3.468 3.464 3.460 3.456 3.453 3.451 3.449 3.447 3.446 3.446 3.446 3.447 3.450 3.451 3.452 3.451 3.447

0.384 0.369 0.356 0.344 0.333 0.324 0.315 0.306 0.298 0.291 0.284 0.277 0.270 0.264 0.258 0.252 0.246 0.240 0.234 0.228 0.223 0.217 0.212 0.206 0.200 0.195 0.189 0.182 0.175 0.167 0.156 0.143 0.130 0.117

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.441 3.437 3.434 3.437 3.442 3.434 3.413 3.389 3.370 3.356 3.344 3.334 3.325 3.317 3.309 3.303 3.296 3.290 3.284 3.279 3.274 3.269 3.265 3.260 3.256 3.252 3.249 3.245 3.242 3.238 3.235 3.232 3.229

0.106 9.67 × 8.97 × 8.22 × 6.38 × 3.09 × 7.52 × 1.23 × 4.37 × 2.38 × 1.30 × 6.90 × 3.48 × 1.71 × 7.99 × 3.64 × 1.60 × 6.76 × 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−4 10−4 10−4 10−5 10−5 10−5 10−6 10−6 10−6 10−7

8 Inorganic Semiconductors and Passivation Layers

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8.2.17 AlSb Data: unpublished results of C. M. Herzinger. These AlSb optical constants are the result of a multiple data set analysis [2]. The data sets came from values compiled in a handbook edited by E. D. Palik [3] originally from ellipsometry results [25] and another compilation [19]. The analysis procedure is described in the Ge section in this chapter (Fig. 8.17, Tables 8.47 and 8.48).

Fig. 8.17 Dielectric function and absorption coefficient of AlSb at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.47 Tauc-Lorentz parameters of (8.1) and (8.2) for AlSb Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j j j j

2.833 0.374 2.848 3.397 39.236 9.944 170.565 58.527 47.559 23.300 10.187 230.634 84.958

0.289 0.114 0.651 0.286 0.500 0.332 0.259 0.437 0.818 0.510 0.324 0.507 0.766

1.628 1.630 1.851 2.244 2.370 2.598 2.829 3.210 3.681 3.999 4.166 4.517 5.127

1.584 1.549 1.562 1.719 2.071 1.964 2.435 2.230 1.918 2.000 2.000 4.337 4.466

0.921 0 0 0 0 0 0 0 0 0 0 0 0

= = = = = = = = = = = = =

1 2 3 4 5 6 7 8 9 10 11 12 13

368

A. Nakane et al.

Table 8.48 Optical constants of AlSb. The optical data, obtained by C. M. Herzinger, are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.236 3.543 3.740 3.867 3.951 4.005 4.042 4.074 4.102 4.123 4.132 4.133 4.138 4.163 4.225 4.339 4.492 4.640 4.737 4.770 4.756 4.671 4.659 4.937 5.319 5.338 5.118 4.921 4.784 4.676 4.584 4.503 4.431 4.368

4.236 3.997 3.756 3.539 3.350 3.188 3.054 2.941 2.841 2.749 2.671 2.616 2.589 2.590 2.608 2.617 2.576 2.465 2.305 2.141 2.004 1.859 1.899 1.951 1.619 1.090 0.763 0.616 0.525 0.451 0.388 0.335 0.290 0.250

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

4.311 4.259 4.211 4.155 4.094 4.038 3.989 3.945 3.906 3.872 3.842 3.814 3.789 3.765 3.744 3.724 3.705 3.687 3.670 3.654 3.639 3.624 3.610 3.596 3.582 3.570 3.558 3.547 3.536 3.527 3.518 3.509 3.501 3.493

0.213 0.177 0.140 0.101 7.45 × 5.84 × 4.85 × 4.20 × 3.76 × 3.43 × 3.15 × 2.89 × 2.64 × 2.39 × 2.14 × 1.90 × 1.66 × 1.42 × 1.19 × 9.66 × 7.44 × 5.26 × 3.16 × 1.40 × 3.77 × 5.01 × 2.61 × 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.485 3.478 3.471 3.464 3.458 3.452 3.446 3.441 3.436 3.430 3.425 3.421 3.416 3.412 3.407 3.403 3.399 3.395 3.392 3.388 3.385 3.381 3.378 3.375 3.372 3.369 3.366 3.363 3.361 3.358 3.356 3.353 3.351

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−4 10−5 10−6

8 Inorganic Semiconductors and Passivation Layers

369

8.2.18 ZnS Data from S. Adachi [26]. The optical data extracted from a zincblende ZnS crystal are shown (Fig. 8.18, Tables 8.49 and 8.50).

Fig. 8.18 Dielectric function and absorption coefficient of a zincblende ZnS crystal at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.49 Tauc-Lorentz parameters of (8.1) and (8.2) for ZnS (zincblende) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

536.939 163.081 124.994 65.058 16.558

0.030 0.306 2.128 1.435 0.028

3.560 3.638 3.789 5.689 5.820

3.560 3.492 3.532 3.565 4.054

2.044 0 0 0 0

= = = = =

1 2 3 4 5

Table 8.50 Optical constants of ZnS (zincblende) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

300 305 310 315 320 325 330 335 340

2.825 2.820 2.817 2.820 2.830 2.853 2.894 2.945 2.974

0.447 0.431 0.417 0.406 0.399 0.389 0.368 0.315 0.220

540 550 560 570 580 590 600 610 620

2.380 2.374 2.369 2.364 2.359 2.355 2.351 2.347 2.343

0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960

n

k

2.293 0 2.292 0 2.291 0 2.290 0 2.289 0 2.288 0 2.287 0 2.286 0 2.285 0 (continued)

370

A. Nakane et al.

Table 8.50 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.958 2.871 2.789 2.738 2.700 2.670 2.645 2.623 2.604 2.586 2.571 2.557 2.532 2.510 2.492 2.476 2.461 2.448 2.437 2.426 2.417 2.408 2.400 2.393 2.386

0.114 0.014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.340 2.337 2.334 2.331 2.328 2.325 2.323 2.321 2.318 2.316 2.314 2.312 2.310 2.309 2.307 2.305 2.304 2.302 2.301 2.300 2.298 2.297 2.296 2.295 2.294

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.285 2.284 2.283 2.282 2.282 2.281 2.280 2.280 2.279 2.279 2.278 2.278 2.277 2.276 2.276 2.276 2.275 2.275 2.274 2.274 2.273 2.273 2.272 2.272

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8.2.19 ZnSe To express the dielectric function of a ZnSe zincblende crystal, two separate data sets are used depending on the energy region: (i) Data of J. Lee, R. W. Collins, A. R. Heyd, F. Flack and N. Samarth [27] for E ≥ 1.5 eV, (ii) Data of D. T. F. Marple [28] for E < 1.5 eV. The optical data have been extracted from an epitaxial ZnSe layer formed on a GaAs substrate [27] and a ZnSe crystal formed by sublimation [28] (Fig. 8.19, Tables 8.51 and 8.52).

8 Inorganic Semiconductors and Passivation Layers

371

Fig. 8.19 Dielectric function and absorption coefficient of ZnSe at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.51 Tauc-Lorentz parameters of (8.1) and (8.2) for ZnSe Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

447.567 37.872 1.492 10.447 1.016 53.016 3.281 228.551

0.051 1.332 0.211 0.492 0.171 2.193 0.273 0.113

2.672 3.113 3.181 4.770 4.833 4.836 5.086 5.622

2.667 2.667 2.667 2.667 2.667 2.667 3.081 5.004

2.473 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 8.52 Optical constants of ZnSe calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

300 305 310 315 320 325 330 335

3.174 3.144 3.117 3.092 3.069 3.049 3.031 3.015

0.641 0.600 0.564 0.533 0.506 0.482 0.460 0.441

540 550 560 570 580 590 600 610

2.655 2.643 2.632 2.623 2.614 2.606 2.598 2.591

0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950

n

k

2.501 0 2.500 0 2.498 0 2.497 0 2.495 0 2.494 0 2.492 0 2.491 0 (continued)

372

A. Nakane et al.

Table 8.52 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.000 2.988 2.978 2.968 2.960 2.953 2.946 2.941 2.938 2.939 2.944 2.944 2.937 2.914 2.890 2.870 2.857 2.863 2.919 2.824 2.776 2.744 2.720 2.700 2.683 2.668

0.424 0.408 0.392 0.378 0.364 0.350 0.337 0.326 0.315 0.304 0.287 0.262 0.238 0.201 0.175 0.157 0.146 0.140 9.04 × 10−2 0 0 0 0 0 0 0

620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.585 2.579 2.573 2.568 2.563 2.558 2.554 2.550 2.546 2.542 2.539 2.536 2.532 2.529 2.527 2.524 2.521 2.519 2.517 2.514 2.512 2.510 2.508 2.506 2.505 2.503

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.490 2.489 2.488 2.487 2.485 2.484 2.483 2.482 2.482 2.481 2.480 2.479 2.478 2.477 2.476 2.476 2.475 2.474 2.474 2.473 2.472 2.472 2.471 2.470 2.470

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8.2.20 ZnTe Data from S. Adachi [26]. The optical data of a single ZnTe crystal are shown (Fig. 8.20, Tables 8.53 and 8.54).

8 Inorganic Semiconductors and Passivation Layers

373

Fig. 8.20 Dielectric function and absorption coefficient of ZnTe at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.53 Tauc-Lorentz parameters of (8.1) and (8.2) for ZnTe Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

1687.93 81.164 89.180 11.054 11.900 56.504

0.017 1.094 1.315 0.257 0.474 1.419

2.267 2.267 3.491 3.584 4.137 5.172

2.267 2.267 2.659 2.267 2.267 2.430

1.061 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

Table 8.54 Optical constants of ZnTe calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370

3.331 3.435 3.461 3.437 3.400 3.372 3.375 3.446 3.632 3.896 4.064 4.085 4.039 3.979 3.921

1.998 1.862 1.726 1.632 1.588 1.592 1.642 1.728 1.792 1.709 1.470 1.227 1.049 0.924 0.829

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680

3.335 3.291 3.204 3.156 3.120 3.091 3.067 3.045 3.026 3.009 2.994 2.980 2.967 2.955 2.944

0.189 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020

2.819 0 2.815 0 2.812 0 2.808 0 2.805 0 2.802 0 2.799 0 2.796 0 2.794 0 2.791 0 2.788 0 2.786 0 2.784 0 2.781 0 2.779 0 (continued)

k

374

A. Nakane et al.

Table 8.54 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.869 3.821 3.776 3.734 3.694 3.656 3.586 3.524 3.471 3.426 3.389 3.359 3.336 3.318 3.303 3.289 3.279 3.273 3.281

0.754 0.691 0.636 0.589 0.547 0.511 0.453 0.408 0.375 0.349 0.328 0.311 0.295 0.279 0.262 0.245 0.229 0.217 0.207

690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.933 2.924 2.915 2.906 2.898 2.891 2.884 2.877 2.871 2.865 2.859 2.854 2.849 2.844 2.839 2.835 2.830 2.826 2.822

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.777 2.775 2.773 2.771 2.769 2.767 2.766 2.764 2.762 2.761 2.759 2.758 2.756 2.755 2.753 2.752 2.751 2.750

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8.2.21 CdS Data from J. Li, J. Chen and R. W. Collins [29]. The optical data of a polycrystalline CdS layer prepared by sputtering at 310 °C are shown (Fig. 8.21, Tables 8.55 and 8.56).

Fig. 8.21 Dielectric function and absorption coefficient of CdS at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

8 Inorganic Semiconductors and Passivation Layers

375

Table 8.55 Tauc-Lorentz parameters of (8.1) and (8.2) for CdS Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

28.655 7.388 147.591 162.769 0.093 28.082 2.059 16.217 251.674

0.124 0.307 0.440 5.572 0.200 1.044 0.349 0.638 1.963

2.463 2.583 2.588 2.980 3.395 4.772 4.888 5.366 5.781

2.342 1.985 2.585 2.775 2.397 3.404 2.408 3.789 5.601

0.968 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.56 Optical constants of CdS calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

2.718 2.701 2.686 2.673 2.662 2.652 2.644 2.637 2.631 2.625 2.620 2.616 2.614 2.614 2.614 2.612 2.609 2.607 2.605 2.603 2.602 2.602 2.605 2.610 2.617 2.626

0.630 0.607 0.587 0.570 0.554 0.540 0.527 0.514 0.503 0.492 0.483 0.474 0.466 0.458 0.447 0.437 0.427 0.419 0.412 0.405 0.399 0.388 0.378 0.367 0.356 0.345

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

2.622 2.591 2.566 2.544 2.526 2.509 2.495 2.482 2.471 2.461 2.452 2.443 2.436 2.429 2.422 2.416 2.411 2.405 2.400 2.396 2.391 2.387 2.383 2.380 2.376 2.373

1.92 1.21 7.52 4.54 2.61 1.37 6.10 1.92 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

× × × × × × × ×

10−2 10−2 10−3 10−3 10−3 10−3 10−4 10−4

λ (nm)

n

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

2.349 0 2.347 0 2.345 0 2.343 0 2.341 0 2.340 0 2.338 0 2.336 0 2.335 0 2.333 0 2.332 0 2.330 0 2.329 0 2.328 0 2.326 0 2.325 0 2.324 0 2.323 0 2.322 0 2.321 0 2.320 0 2.319 0 2.318 0 2.317 0 2.316 0 2.315 0 (continued)

k

376

A. Nakane et al.

Table 8.56 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

460 470 480 490 500 510 520 530

2.635 2.650 2.677 2.720 2.776 2.781 2.714 2.660

0.334 0.327 0.319 0.294 0.241 0.120 5.30 × 10−2 3.02 × 10−2

800 810 820 830 840 850 860 870

2.370 2.367 2.364 2.361 2.359 2.356 2.354 2.351

0 0 0 0 0 0 0 0

1140 1150 1160 1170 1180 1190 1200

2.314 2.313 2.312 2.312 2.311 2.310 2.309

0 0 0 0 0 0 0

8.2.22 CdSe Data from S. Adachi [26]. The optical data of a wurtzite CdSe single crystal are shown. The wurtzite CdSe crystal has uniaxial optical anisotropy, but the optical properties are almost isotropic at E < 4 eV. Here, the optical constants for the electric field perpendicular to the c axis (E⊥c: ordinary ray) are indicated. The optical constants of the cubic CdSe phase are quite similar to those of the wurtzite phase described here (Fig. 8.22, Tables 8.57 and 8.58).

Fig. 8.22 Dielectric function and absorption coefficient of CdSe (wurtzite) at room temperature. The optical data for ordinary ray (E⊥c) in CdSe are shown. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

8 Inorganic Semiconductors and Passivation Layers

377

Table 8.57 Tauc-Lorentz parameters for the ordinary ray in CdSe (wurtzite) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

324.484 22.872 15.818 2.913 4.050 3.212 137.812

0.063 1.364 4.567 0.438 0.454 0.608 9.534

1.700 2.160 2.285 4.119 4.434 4.789 5.539

1.700 1.706 1.700 1.700 2.874 1.700 2.391

0.376 0 0 0 0 0 0

= = = = = = =

1 2 3 4 5 6 7

Table 8.58 Optical constants for the ordinary ray in CdSe (wurtzite) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430

2.919 2.990 3.016 3.006 2.980 2.952 2.925 2.901 2.880 2.862 2.847 2.833 2.821 2.810 2.800 2.791 2.782 2.774 2.767 2.761 2.755 2.744 2.734 2.727

1.240 1.147 1.036 0.940 0.866 0.812 0.770 0.737 0.710 0.686 0.666 0.648 0.631 0.616 0.601 0.588 0.576 0.565 0.554 0.544 0.535 0.518 0.504 0.491

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770

2.735 2.742 2.747 2.752 2.756 2.760 2.762 2.765 2.767 2.770 2.774 2.780 2.788 2.800 2.817 2.842 2.877 2.923 2.954 2.866 2.807 2.773 2.748 2.728

0.401 0.390 0.378 0.366 0.353 0.341 0.330 0.319 0.309 0.301 0.294 0.287 0.282 0.276 0.269 0.259 0.240 0.196 9.51 × 10−2 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110

2.618 0 2.612 0 2.606 0 2.601 0 2.596 0 2.592 0 2.588 0 2.583 0 2.580 0 2.576 0 2.572 0 2.569 0 2.566 0 2.563 0 2.560 0 2.557 0 2.554 0 2.552 0 2.549 0 2.547 0 2.544 0 2.542 0 2.540 0 2.538 0 (continued)

k

378

A. Nakane et al.

Table 8.58 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

440 450 460 470 480 490 500 510 520 530

2.720 2.716 2.713 2.711 2.711 2.712 2.714 2.717 2.722 2.728

0.480 0.470 0.462 0.454 0.446 0.439 0.432 0.425 0.418 0.410

780 790 800 810 820 830 840 850 860 870

2.711 2.697 2.684 2.673 2.663 2.654 2.645 2.638 2.630 2.624

0 0 0 0 0 0 0 0 0 0

1120 1130 1140 1150 1160 1170 1180 1190 1200

2.536 2.534 2.532 2.530 2.529 2.527 2.525 2.524 2.522

0 0 0 0 0 0 0 0 0

8.2.23 CdTe Data: unpublished results of J. Li and R. W. Collins. The optical data of a polycrystalline CdTe layer processed with post CdCl2/annealing treatments are shown (see also Chap. 13 in Vol. 1) (Fig. 8.23, Tables 8.59 and 8.60).

Fig. 8.23 Dielectric function and absorption coefficient of CdTe at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

8 Inorganic Semiconductors and Passivation Layers

379

Table 8.59 Tauc-Lorentz parameters of (8.1) and (8.2) for CdTe Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j

0.396 × 10−3 19.762 0.681 93.077 4.023 85.342 41.876 2.648 6.673 5.554

0.039 0.479 0.036 0.060 0.276 5.904 1.791 0.352 0.715 0.480

1.379 1.479 1.489 1.489 3.301 3.432 3.506 3.858 4.962 5.181

1.262 1.458 1.369 1.483 1.481 1.671 2.382 1.604 1.795 2.224

1.329 0 0 0 0 0 0 0 0 0

= = = = = = = = = =

1 2 3 4 5 6 7 8 9 10

Table 8.60 Optical constants of CdTe. The optical data obtained by J. Li and R. W. Collins are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430

2.560 2.586 2.652 2.770 2.911 3.010 3.055 3.066 3.060 3.045 3.030 3.025 3.049 3.126 3.270 3.447 3.581 3.637 3.636 3.607 3.570 3.498 3.440 3.394

1.611 1.667 1.732 1.773 1.746 1.659 1.566 1.490 1.437 1.407 1.403 1.427 1.479 1.544 1.577 1.523 1.385 1.221 1.077 0.967 0.883 0.768 0.691 0.632

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770

3.144 3.129 3.115 3.102 3.090 3.078 3.067 3.056 3.046 3.036 3.028 3.019 3.012 3.005 2.998 2.993 2.988 2.984 2.981 2.979 2.978 2.979 2.980 2.983

0.314 0.297 0.282 0.269 0.256 0.244 0.233 0.224 0.215 0.206 0.199 0.192 0.186 0.180 0.175 0.170 0.166 0.162 0.159 0.156 0.152 0.148 0.144 0.140

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110

2.915 2.902 2.892 2.882 2.874 2.866 2.859 2.852 2.846 2.841 2.836 2.831 2.826 2.821 2.817 2.813 2.809 2.806 2.802 2.799 2.796 2.793 2.790 2.787

1.25 × 10−4 4.17 × 10−5 1.55 × 10−5 5.67 × 10−6 2.08 × 10−6 6.87 × 10−7 3.16 × 10−7 1.15 × 10−7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (continued)

380

A. Nakane et al.

Table 8.60 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

440 450 460 470 480 490 500 510 520 530

3.357 3.325 3.297 3.272 3.250 3.229 3.210 3.192 3.175 3.159

0.584 0.543 0.507 0.474 0.445 0.418 0.394 0.371 0.350 0.331

780 790 800 810 820 830 840 850 860 870

2.988 2.994 3.003 3.015 3.029 3.030 3.003 2.972 2.948 2.930

0.134 0.127 0.117 0.103 7.73 × 3.50 × 1.10 × 3.52 × 1.08 × 3.76 ×

1120 1130 1140 1150 1160 1170 1180 1190 1200

2.784 2.782 2.779 2.777 2.774 2.772 2.770 2.768 2.766

0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−3 10−3 10−4

8.2.24 CuInSe2 Data from S. Minoura, T. Maekawa, K. Kodera, A. Nakane, S. Niki and H. Fujiwara [30] (see also Fig. 10.7a in Vol. 1). The optical data of a chalcopyrite CuInSe2 polycrystal (Cu/In = 0.86) prepared by a single co-evaporation process at 520 °C are shown. Although a CuInSe2 single crystal exhibits notable uniaxial anisotropy at E > 2.5 eV, the optical properties are isotropic in CuInSe2 polycrystals.

Fig. 8.24 Dielectric function and absorption coefficient of CuInSe2 (chalcopyrite) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

8 Inorganic Semiconductors and Passivation Layers

381

Table 8.61 Tauc-Lorentz parameters of (8.1) and (8.2) for CuInSe2 (chalcopyrite). The model parameters reported by Minoura et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

12.255 14.580 21.014 13.185 58.905 35.077 12.440 7.692 54.873

0.175 1.087 2.446 0.802 0.425 1.332 1.129 0.928 3.381

0.996 1.281 1.860 2.909 3.050 3.599 4.709 5.216 6.399

0.947 1.001 1.438 1.485 3.017 2.593 2.013 2.324 2.948

1.342 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.62 Optical constants of CuInSe2 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430

2.812 2.799 2.791 2.787 2.787 2.790 2.796 2.803 2.811 2.817 2.822 2.826 2.829 2.832 2.836 2.841 2.849 2.860 2.873 2.889 2.906 2.951 3.020 3.089

1.082 1.065 1.053 1.044 1.036 1.029 1.020 1.011 1.000 0.989 0.977 0.967 0.959 0.953 0.950 0.949 0.949 0.951 0.952 0.952 0.953 0.956 0.945 0.902

560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

3.017 3.005 2.995 2.985 2.977 2.970 2.964 2.959 2.954 2.950 2.946 2.943 2.941 2.938 2.937 2.935 2.933 2.932 2.931 2.931 2.930 2.930 2.929 2.929

0.368 0.358 0.350 0.342 0.335 0.329 0.324 0.318 0.313 0.308 0.304 0.299 0.295 0.291 0.286 0.282 0.278 0.274 0.270 0.266 0.263 0.259 0.255 0.251

920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150

2.939 2.940 2.941 2.941 2.942 2.942 2.942 2.942 2.942 2.941 2.941 2.940 2.939 2.938 2.938 2.937 2.937 2.936 2.936 2.937 2.937 2.938 2.939 2.941

0.200 0.195 0.190 0.185 0.180 0.175 0.170 0.165 0.160 0.155 0.150 0.146 0.142 0.138 0.134 0.130 0.126 0.123 0.120 0.116 0.113 0.110 0.106 0.102 (continued)

382

A. Nakane et al.

Table 8.62 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

440 450 460 470 480 490 500 510 520 530 540 550

3.143 3.174 3.184 3.178 3.163 3.144 3.123 3.102 3.082 3.063 3.046 3.031

0.836 0.761 0.687 0.621 0.565 0.520 0.483 0.453 0.429 0.409 0.393 0.379

800 810 820 830 840 850 860 870 880 890 900 910

2.929 2.929 2.929 2.929 2.930 2.930 2.931 2.932 2.934 2.935 2.937 2.938

0.247 0.244 0.240 0.236 0.233 0.229 0.226 0.222 0.219 0.214 0.210 0.205

1160 1170 1180 1190 1200 1220 1240 1260 1280 1300

2.942 2.944 2.946 2.947 2.948 2.947 2.940 2.928 2.912 2.895

9.68 9.14 8.52 7.80 7.00 5.19 3.31 1.68 5.60 0

× × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3

8.2.25 CuGaSe2 Data from S. Minoura, T. Maekawa, K. Kodera, A. Nakane, S. Niki and H. Fujiwara [30] (see also Fig. 10.7a in Vol. 1). The optical data of a chalcopyrite CuGaSe2 polycrystal (Cu/Ga = 0.84) prepared by a single co-evaporation process at 520 °C are shown. Although a CuGaSe2 single crystal exhibits uniaxial anisotropy, the optical properties are isotropic in CuGaSe2 polycrystals.

Fig. 8.25 Dielectric function and absorption coefficient of CuGaSe2 (chalcopyrite) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

8 Inorganic Semiconductors and Passivation Layers

383

Table 8.63 Tauc-Lorentz parameters of (8.1) and (8.2) for CuGaSe2 (chalcopyrite). The model parameters reported by Minoura et al. are summarized Peak j=1 j=2 j=3 j=4 j=5 j=6 j=7 j=8 j=9

A (eV) 13.966 34.567 22.058 41.486 18.203 107.550 14.859 55.933 51.600

C (eV) 0.252 1.162 0.946 0.487 0.733 0.955 1.286 0.592 3.063

E0 (eV) 1.713 1.855 3.024 3.227 3.582 3.970 5.104 5.759 6.729

ε1(∞) 1.202 0 0 0 0 0 0 0 0

Eg (eV) 1.626 1.728 2.098 2.678 2.659 3.441 1.946 4.973 3.245

Table 8.64 Optical constants of CuGaSe2 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.899 2.922 2.937 2.942 2.939 2.931 2.925 2.924 2.930 2.943 2.962 2.986 3.018 3.061 3.116 3.179 3.242 3.297 3.335 3.355 3.359 3.341 3.310 3.275 3.239 3.202 3.167 3.135 3.107 3.082 3.060 3.041 3.026 3.013

1.197 1.163 1.126 1.089 1.060 1.040 1.031 1.030 1.034 1.038 1.043 1.050 1.057 1.062 1.057 1.038 1.000 0.942 0.872 0.800 0.731 0.618 0.532 0.463 0.407 0.363 0.329 0.302 0.281 0.264 0.251 0.239 0.229 0.220

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.002 2.993 2.985 2.978 2.972 2.966 2.961 2.956 2.950 2.944 2.937 2.930 2.924 2.918 2.912 2.907 2.902 2.895 2.886 2.874 2.860 2.845 2.830 2.819 2.809 2.801 2.793 2.786 2.780 2.774 2.769 2.763 2.758 2.754

0.212 0.203 0.194 0.185 0.175 0.165 0.155 0.144 0.133 0.122 0.112 0.102 9.28 × 8.39 × 7.50 × 6.54 × 5.46 × 4.22 × 2.95 × 1.74 × 7.91 × 2.20 × 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.750 2.745 2.742 2.738 2.734 2.731 2.728 2.725 2.722 2.719 2.716 2.714 2.711 2.709 2.707 2.704 2.702 2.700 2.698 2.696 2.694 2.693 2.691 2.689 2.688 2.686 2.685 2.683 2.682 2.680 2.679 2.678 2.676

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

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A. Nakane et al.

8.2.26 CuIn1−xGaxSe2 [Cu/(In + Ga) = 0.90] The dielectric functions of CuIn1−xGaxSe2 chalcopyrite polycrystalline alloys with different Ga composition x are summarized. These dielectric functions were obtained originally from an established optical database in which the Cu(In,Ga)Se2 optical constants for arbitrary Cu and Ga compositions can be deduced by applying the energy shift model and spectral averaging method [Sect. 10.4 (Fig. 10.18) in Vol. 1] (see also S. Minoura, T. Maekawa, K. Kodera, A. Nakane, S. Niki and H. Fujiwara [30]). Based on this method, various CuIn1−xGaxSe2 dielectric functions (x = 0.1– 0.9) with a fixed Cu composition [Cu/(In + Ga) = 0.90] were calculated using the dielectric functions of CuInSe2 (Fig. 8.24) and CuGaSe2 (Fig. 8.25). The dielectric functions obtained from this procedure have been parameterized further using the Tauc-Lorentz model and the modeled results are described here. The Tauc-Lorentz parameters and optical constants of x = 0.0 (CuInSe2) and x = 1.0 (CuGaSe2) are shown in Tables 8.61, 8.62, 8.63 and 8.64 (Fig. 8.26, Tables 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72, 8.73, 8.74, 8.75, 8.76, 8.77, 8.78, 8.79, 8.80, 8.81 and 8.82).

Fig. 8.26 Dielectric functions, optical constants and absorption coefficients of various polycrystalline CuIn1−xGaxSe2 alloys [Cu/(In + Ga) = 0.90] calculated by the Tauc-Lorentz model [(8.1) and (8.2)]. The dielectric functions of x = 0.0 and x = 1.0 correspond to those shown in Figs. 8.24 and 8.25, respectively

8 Inorganic Semiconductors and Passivation Layers

385

Table 8.65 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.1) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

14.853 18.161 21.968 14.544 22.096 33.335 9.890 7.383 46.334

0.219 1.014 2.512 0.783 0.350 1.253 1.114 0.840 3.437

1.068 1.318 2.002 2.943 3.145 3.632 4.777 5.299 6.478

1.020 1.123 1.503 1.593 3.039 2.626 1.659 2.615 2.523

1.369 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.66 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.2) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

15.475 10.059 33.548 19.566 3.749 38.388 9.945 6.285 37.065

0.246 0.610 3.756 0.735 0.404 1.074 1.062 0.781 3.364

1.145 1.370 2.294 2.970 3.251 3.642 4.822 5.374 6.561

1.093 1.194 1.334 1.886 2.789 2.902 1.845 2.621 2.149

1.380 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.67 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.3) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

21.463 15.793 17.913 30.709 3.545 60.430 8.539 8.083 40.809

0.321 0.652 2.320 0.703 0.580 0.983 1.049 0.750 3.286

1.207 1.415 2.815 2.977 3.252 3.650 4.873 5.441 6.564

1.171 1.363 1.291 2.204 2.394 3.141 1.577 3.021 2.319

1.382 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

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Table 8.68 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.4) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

20.119 17.816 17.292 31.278 4.029 91.535 7.514 7.366 40.931

0.292 0.636 2.088 0.677 0.860 0.901 1.019 0.727 3.189

1.311 1.504 2.769 3.008 3.336 3.662 4.919 5.511 6.588

1.254 1.430 1.366 2.272 1.746 3.302 1.436 2.970 2.367

1.374 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.69 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.5) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

15.363 19.581 36.688 42.958 3.898 81.053 9.899 6.757 45.498

0.245 0.825 2.475 0.762 0.594 0.918 1.056 0.739 3.084

1.381 1.623 2.677 3.056 3.403 3.712 4.936 5.564 6.615

1.308 1.411 1.741 2.328 2.904 3.342 1.852 2.832 2.776

1.336 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.70 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.6) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

16.750 19.946 22.586 55.205 3.644 79.176 7.673 3.544 48.704

0.184 0.958 1.661 0.900 0.659 1.037 1.081 0.752 3.193

1.419 1.644 2.554 3.086 3.142 3.773 4.960 5.623 6.655

1.377 1.413 1.795 2.375 2.224 3.296 1.392 1.708 2.777

1.316 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

8 Inorganic Semiconductors and Passivation Layers

387

Table 8.71 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.7) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1

21.037

0.213

1.489

1.444

1.283

j=2

35.604

0.889

1.554

1.552

0

j=3

22.060

1.682

2.809

1.852

0

j=4

50.790

0.771

3.120

2.435

0

j=5

3.847

0.857

3.420

2.488

0

j=6

81.395

1.056

3.828

3.306

0

j=7

8.338

1.101

4.988

1.491

0

j=8

5.241

0.725

5.668

2.541

0

j=9

51.167

3.227

6.663

2.889

0

Table 8.72 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.8) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

29.218 37.482 20.700 44.971 8.127 99.920 11.027 14.165 52.886

0.229 1.205 1.226 0.637 0.642 1.059 1.147 0.676 3.202

1.526 1.623 2.953 3.157 3.491 3.858 5.021 5.699 6.666

1.514 1.617 1.967 2.533 2.624 3.328 1.827 3.924 3.053

1.247 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 8.73 Tauc-Lorentz parameters of (8.1) and (8.2) for CuIn1−xGaxSe2 (x = 0.9) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

28.319 38.663 24.561 31.780 13.690 104.073 15.900 51.960 43.761

0.321 1.173 1.109 0.512 0.726 0.979 1.246 0.633 3.092

1.594 1.731 3.045 3.194 3.536 3.916 5.068 5.708 6.785

1.572 1.735 2.056 2.597 2.602 3.405 2.122 4.851 2.935

1.243 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

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Table 8.74 Optical constants of CuIn1−xGaxSe2 (x = 0.1) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.794 2.784 2.779 2.778 2.782 2.788 2.797 2.805 2.813 2.818 2.822 2.824 2.825 2.827 2.831 2.838 2.850 2.865 2.885 2.907 2.933 3.001 3.079 3.146 3.188 3.205 3.203 3.189 3.169 3.146 3.124 3.103 3.083 3.065

1.079 1.067 1.058 1.051 1.045 1.038 1.029 1.018 1.006 0.993 0.982 0.973 0.967 0.964 0.965 0.969 0.975 0.980 0.984 0.987 0.990 0.985 0.951 0.887 0.807 0.725 0.651 0.589 0.538 0.497 0.464 0.438 0.416 0.399

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.049 3.035 3.023 3.012 3.003 2.994 2.987 2.981 2.975 2.970 2.966 2.962 2.958 2.955 2.953 2.951 2.949 2.947 2.946 2.945 2.944 2.943 2.943 2.943 2.943 2.943 2.943 2.943 2.944 2.945 2.946 2.947 2.948 2.949

0.384 0.371 0.361 0.351 0.343 0.335 0.328 0.321 0.315 0.309 0.304 0.298 0.293 0.288 0.283 0.279 0.274 0.269 0.265 0.261 0.256 0.252 0.248 0.243 0.239 0.235 0.231 0.226 0.222 0.218 0.213 0.208 0.203 0.197

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210

2.950 2.950 2.950 2.950 2.950 2.950 2.949 2.948 2.947 2.946 2.945 2.945 2.944 2.943 2.943 2.942 2.942 2.943 2.943 2.944 2.945 2.945 2.946 2.946 2.946 2.944 2.941 2.937 2.931 2.924 2.916 2.907 2.898 2.890

0.192 0.186 0.180 0.174 0.169 0.163 0.157 0.152 0.147 0.142 0.137 0.132 0.128 0.123 0.119 0.115 0.110 0.106 0.101 9.61 × 9.04 × 8.41 × 7.72 × 6.96 × 6.11 × 5.19 × 4.24 × 3.30 × 2.41 × 1.63 × 9.85 × 4.98 × 1.79 × 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

389

Table 8.75 Optical constants of CuIn1−xGaxSe2 (x = 0.2) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.778 2.771 2.769 2.772 2.779 2.789 2.799 2.808 2.814 2.818 2.819 2.818 2.818 2.820 2.827 2.839 2.856 2.879 2.906 2.938 2.976 3.059 3.139 3.195 3.224 3.227 3.215 3.194 3.170 3.146 3.123 3.103 3.084 3.068

1.080 1.071 1.065 1.060 1.054 1.046 1.035 1.022 1.008 0.995 0.985 0.978 0.977 0.980 0.988 0.997 1.006 1.014 1.020 1.023 1.022 0.998 0.941 0.859 0.770 0.687 0.615 0.558 0.512 0.476 0.448 0.424 0.405 0.389

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.054 3.041 3.030 3.020 3.011 3.003 2.997 2.991 2.985 2.980 2.976 2.972 2.969 2.966 2.964 2.962 2.960 2.959 2.957 2.957 2.956 2.956 2.956 2.956 2.956 2.956 2.957 2.957 2.958 2.958 2.958 2.958 2.958 2.958

0.375 0.363 0.352 0.342 0.333 0.325 0.318 0.310 0.304 0.297 0.291 0.285 0.280 0.275 0.269 0.264 0.259 0.254 0.249 0.244 0.240 0.235 0.230 0.225 0.219 0.214 0.209 0.203 0.197 0.191 0.184 0.178 0.171 0.165

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.957 2.955 2.954 2.953 2.951 2.949 2.948 2.947 2.947 2.947 2.946 2.947 2.947 2.947 2.947 2.946 2.945 2.943 2.940 2.935 2.929 2.922 2.913 2.904 2.894 2.886 2.878 2.872 2.867 2.862 2.857 2.853 2.849

0.158 0.152 0.146 0.140 0.134 0.129 0.124 0.120 0.115 0.110 0.104 9.88 × 9.27 × 8.61 × 7.88 × 7.08 × 6.22 × 5.29 × 4.33 × 3.37 × 2.46 × 1.65 × 9.84 × 4.86 × 1.64 × 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3

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Table 8.76 Optical constants of CuIn1−xGaxSe2 (x = 0.3) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.764 2.761 2.763 2.770 2.781 2.792 2.803 2.811 2.815 2.815 2.813 2.810 2.811 2.816 2.828 2.847 2.874 2.907 2.945 2.987 3.033 3.124 3.197 3.239 3.251 3.241 3.220 3.195 3.170 3.146 3.124 3.105 3.088 3.072

1.086 1.080 1.076 1.071 1.064 1.053 1.040 1.025 1.011 0.999 0.992 0.991 0.996 1.006 1.020 1.033 1.045 1.053 1.057 1.054 1.044 0.996 0.917 0.821 0.727 0.647 0.581 0.530 0.490 0.459 0.433 0.411 0.393 0.378

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.059 3.047 3.036 3.027 3.020 3.012 3.006 3.000 2.995 2.990 2.986 2.982 2.979 2.976 2.974 2.972 2.971 2.970 2.969 2.969 2.968 2.968 2.969 2.969 2.969 2.969 2.968 2.967 2.967 2.965 2.964 2.962 2.960 2.958

0.364 0.352 0.342 0.332 0.323 0.314 0.306 0.298 0.291 0.284 0.277 0.271 0.265 0.260 0.254 0.249 0.243 0.238 0.232 0.226 0.221 0.214 0.208 0.201 0.194 0.187 0.180 0.173 0.165 0.158 0.151 0.144 0.138 0.131

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.956 2.954 2.953 2.952 2.952 2.952 2.952 2.952 2.952 2.950 2.947 2.943 2.937 2.930 2.921 2.912 2.902 2.891 2.882 2.875 2.869 2.863 2.858 2.853 2.849 2.845 2.841 2.837 2.834 2.831 2.827 2.824 2.822

0.125 0.120 0.115 0.110 0.104 9.77 × 9.04 × 8.22 × 7.32 × 6.35 × 5.33 × 4.29 × 3.28 × 2.34 × 1.52 × 8.51 × 3.64 × 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

391

Table 8.77 Optical constants of CuIn1−xGaxSe2 (x = 0.4) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.752 2.753 2.760 2.771 2.784 2.797 2.806 2.811 2.811 2.807 2.802 2.800 2.804 2.816 2.837 2.867 2.906 2.950 2.998 3.047 3.097 3.187 3.247 3.271 3.268 3.248 3.221 3.194 3.169 3.146 3.126 3.108 3.092 3.077

1.093 1.090 1.086 1.081 1.071 1.058 1.042 1.026 1.012 1.004 1.003 1.011 1.024 1.041 1.059 1.075 1.086 1.089 1.085 1.072 1.050 0.978 0.880 0.777 0.684 0.609 0.551 0.506 0.471 0.442 0.419 0.398 0.381 0.366

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.065 3.054 3.044 3.036 3.028 3.021 3.014 3.008 3.003 2.998 2.994 2.991 2.988 2.986 2.984 2.983 2.982 2.981 2.981 2.981 2.981 2.980 2.979 2.978 2.976 2.974 2.972 2.969 2.966 2.964 2.961 2.959 2.957 2.957

0.353 0.341 0.329 0.319 0.309 0.300 0.291 0.283 0.276 0.269 0.262 0.256 0.249 0.243 0.237 0.231 0.224 0.217 0.210 0.203 0.195 0.187 0.179 0.170 0.162 0.154 0.145 0.138 0.131 0.124 0.117 0.112 0.106 9.99 × 10−2

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.957 2.957 2.957 2.955 2.952 2.946 2.939 2.929 2.918 2.907 2.895 2.885 2.876 2.869 2.863 2.857 2.852 2.847 2.843 2.838 2.835 2.831 2.827 2.824 2.821 2.818 2.815 2.812 2.809 2.807 2.804 2.802 2.799

9.29 8.44 7.45 6.35 5.17 3.96 2.82 1.81 9.92 4.14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

× × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

392

A. Nakane et al.

Table 8.78 Optical constants of CuIn1−xGaxSe2 (x = 0.5) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.787 2.793 2.804 2.817 2.830 2.840 2.846 2.847 2.844 2.840 2.838 2.840 2.850 2.868 2.895 2.931 2.974 3.021 3.071 3.120 3.167 3.240 3.279 3.287 3.272 3.247 3.218 3.189 3.163 3.139 3.117 3.098 3.082 3.067

1.113 1.106 1.098 1.086 1.071 1.053 1.035 1.018 1.007 1.002 1.005 1.014 1.027 1.043 1.058 1.068 1.072 1.068 1.054 1.030 0.997 0.907 0.804 0.704 0.619 0.552 0.499 0.458 0.426 0.400 0.379 0.361 0.345 0.332

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.055 3.044 3.034 3.025 3.017 3.010 3.003 2.997 2.992 2.988 2.984 2.981 2.979 2.977 2.976 2.974 2.973 2.972 2.972 2.971 2.970 2.969 2.967 2.965 2.962 2.959 2.956 2.954 2.951 2.950 2.948 2.947 2.946 2.944

0.321 0.310 0.299 0.289 0.280 0.272 0.264 0.257 0.250 0.244 0.237 0.231 0.225 0.218 0.212 0.205 0.198 0.191 0.184 0.175 0.167 0.158 0.150 0.141 0.133 0.125 0.118 0.111 0.104 9.73 × 9.00 × 8.19 × 7.26 × 6.23 ×

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.941 2.936 2.928 2.918 2.907 2.894 2.883 2.873 2.864 2.857 2.851 2.845 2.840 2.835 2.830 2.826 2.822 2.818 2.815 2.811 2.808 2.805 2.802 2.799 2.796 2.794 2.791 2.789 2.787 2.784 2.782 2.780 2.778

5.10 3.91 2.74 1.70 8.89 3.45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2

× × × × × ×

10−2 10−2 10−2 10−2 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

393

Table 8.79 Optical constants of CuIn1−xGaxSe2 (x = 0.6) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.825 2.836 2.848 2.861 2.872 2.879 2.882 2.881 2.877 2.875 2.876 2.883 2.898 2.923 2.955 2.996 3.044 3.094 3.143 3.188 3.227 3.281 3.301 3.295 3.273 3.243 3.212 3.181 3.153 3.128 3.106 3.086 3.069 3.056

1.128 1.117 1.103 1.086 1.066 1.046 1.027 1.012 1.003 1.001 1.006 1.016 1.028 1.041 1.051 1.056 1.052 1.037 1.012 0.977 0.934 0.833 0.730 0.636 0.558 0.497 0.449 0.412 0.383 0.360 0.341 0.326 0.313 0.302

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.044 3.033 3.023 3.014 3.006 2.999 2.993 2.987 2.982 2.978 2.975 2.972 2.970 2.968 2.967 2.966 2.965 2.964 2.963 2.962 2.960 2.957 2.954 2.951 2.948 2.945 2.942 2.939 2.937 2.935 2.933 2.930 2.924 2.914

0.291 0.281 0.272 0.263 0.255 0.247 0.240 0.233 0.227 0.221 0.214 0.208 0.202 0.195 0.188 0.181 0.174 0.165 0.157 0.148 0.139 0.130 0.122 0.113 0.105 9.75 × 9.00 × 8.25 × 7.45 × 6.57 × 5.54 × 4.35 × 3.05 × 1.79 ×

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.901 2.887 2.874 2.864 2.856 2.848 2.842 2.836 2.831 2.826 2.821 2.816 2.812 2.808 2.805 2.801 2.798 2.795 2.792 2.789 2.786 2.783 2.781 2.778 2.776 2.774 2.771 2.769 2.767 2.765 2.764 2.762 2.760

8.01 × 10−3 1.98 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

394

A. Nakane et al.

Table 8.80 Optical constants of CuIn1−xGaxSe2 (x = 0.7) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.844 2.858 2.874 2.888 2.897 2.902 2.901 2.898 2.895 2.894 2.899 2.911 2.932 2.962 3.000 3.044 3.094 3.145 3.193 3.235 3.269 3.310 3.315 3.297 3.267 3.234 3.202 3.171 3.143 3.118 3.096 3.077 3.061 3.047

1.148 1.132 1.114 1.092 1.068 1.045 1.025 1.012 1.006 1.007 1.014 1.025 1.036 1.046 1.051 1.050 1.038 1.016 0.982 0.940 0.890 0.780 0.674 0.584 0.513 0.458 0.415 0.382 0.355 0.334 0.316 0.302 0.290 0.278

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.034 3.023 3.013 3.004 2.996 2.990 2.984 2.979 2.975 2.972 2.969 2.966 2.964 2.962 2.961 2.959 2.957 2.954 2.951 2.948 2.944 2.941 2.937 2.934 2.930 2.928 2.925 2.922 2.916 2.907 2.893 2.878 2.864 2.854

0.268 0.259 0.250 0.242 0.234 0.227 0.221 0.214 0.207 0.200 0.193 0.186 0.179 0.171 0.163 0.154 0.145 0.136 0.126 0.117 0.109 0.100 9.20 × 8.40 × 7.59 × 6.72 × 5.76 × 4.59 × 3.22 × 1.88 × 7.97 × 1.63 × 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.845 2.838 2.831 2.825 2.819 2.814 2.809 2.804 2.800 2.796 2.792 2.788 2.785 2.782 2.778 2.775 2.772 2.770 2.767 2.765 2.762 2.760 2.758 2.755 2.753 2.751 2.749 2.747 2.746 2.744 2.742 2.741 2.739

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

395

Table 8.81 Optical constants of CuIn1−xGaxSe2 (x = 0.8) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.857 2.876 2.894 2.907 2.915 2.916 2.912 2.907 2.904 2.908 2.918 2.937 2.963 2.996 3.036 3.085 3.138 3.191 3.240 3.280 3.309 3.331 3.320 3.292 3.259 3.225 3.192 3.162 3.133 3.108 3.087 3.068 3.051 3.037

1.170 1.150 1.126 1.098 1.070 1.046 1.027 1.017 1.016 1.020 1.029 1.038 1.046 1.052 1.054 1.048 1.031 1.001 0.959 0.906 0.847 0.727 0.623 0.541 0.477 0.427 0.388 0.356 0.331 0.311 0.295 0.281 0.269 0.258

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.024 3.013 3.004 2.996 2.989 2.983 2.978 2.974 2.970 2.967 2.964 2.961 2.958 2.954 2.951 2.947 2.943 2.939 2.935 2.930 2.926 2.922 2.918 2.914 2.909 2.900 2.888 2.873 2.857 2.846 2.836 2.828 2.821 2.814

0.249 0.240 0.232 0.225 0.217 0.210 0.202 0.194 0.186 0.178 0.169 0.161 0.151 0.142 0.133 0.123 0.114 0.105 9.61 × 8.73 × 7.84 × 6.92 × 5.94 × 4.89 × 3.67 × 2.34 × 1.11 × 2.62 × 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.808 2.803 2.797 2.792 2.788 2.784 2.779 2.776 2.772 2.768 2.765 2.762 2.759 2.756 2.753 2.751 2.748 2.745 2.743 2.741 2.739 2.737 2.735 2.733 2.731 2.729 2.727 2.725 2.724 2.722 2.721 2.719 2.718

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3

396

A. Nakane et al.

Table 8.82 Optical constants of CuIn1−xGaxSe2 (x = 0.9) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.876 2.898 2.917 2.927 2.929 2.925 2.919 2.914 2.916 2.925 2.940 2.962 2.991 3.027 3.074 3.128 3.187 3.243 3.290 3.323 3.341 3.341 3.317 3.285 3.250 3.215 3.181 3.150 3.122 3.097 3.075 3.056 3.039 3.025

1.186 1.160 1.129 1.096 1.066 1.042 1.028 1.023 1.025 1.030 1.037 1.044 1.051 1.056 1.055 1.044 1.020 0.978 0.923 0.858 0.791 0.671 0.575 0.501 0.442 0.395 0.357 0.328 0.305 0.286 0.271 0.258 0.247 0.237

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.013 3.003 2.994 2.987 2.980 2.974 2.969 2.965 2.961 2.956 2.952 2.947 2.942 2.937 2.931 2.926 2.921 2.916 2.912 2.908 2.903 2.895 2.885 2.871 2.856 2.841 2.830 2.821 2.813 2.805 2.799 2.792 2.787 2.781

0.228 0.220 0.211 0.203 0.195 0.186 0.178 0.169 0.160 0.150 0.140 0.130 0.120 0.111 0.102 9.28 × 8.42 × 7.56 × 6.69 × 5.64 × 4.43 × 3.13 × 1.88 × 8.47 × 1.88 × 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.776 2.772 2.767 2.763 2.759 2.756 2.752 2.749 2.745 2.742 2.739 2.736 2.734 2.731 2.729 2.726 2.724 2.722 2.720 2.717 2.716 2.714 2.712 2.710 2.708 2.707 2.705 2.703 2.702 2.700 2.699 2.698 2.696

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

397

8.2.27 CuInGaSe2-Based Compound [Cu/(In + Ga) = 0.69] Data from S. Minoura, T. Maekawa, K. Kodera, A. Nakane, S. Niki and H. Fujiwara [30] (see also Fig. 10.9a in Vol. 1). The optical data of a low-Cu CuIn1−xGax Se2-based polycrystalline layer [Cu/(In + Ga) = 0.69, x = 0.42] prepared by a single co-evaporation process at 520 °C are shown (Fig. 8.27, Tables 8.83 and 8.84).

Fig. 8.27 Dielectric function and absorption coefficient of a CuIn1−xGaxSe2-based compound [Cu/(In + Ga) = 0.69, x = 0.42] at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.83 Tauc-Lorentz parameters of (8.1) and (8.2) for a CuIn1−xGaxSe2-based compound [Cu/(In + Ga) = 0.69, x = 0.42]. The model parameters reported by Minoura et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

15.013 23.516 18.503 21.522 3.420 148.907 7.182 3.674 48.984

0.612 1.791 1.439 0.591 0.687 1.126 1.102 0.775 3.519

1.355 1.595 2.948 2.986 3.332 3.563 4.950 5.532 6.509

1.287 1.453 1.901 2.395 1.428 3.284 1.415 2.477 2.553

1.203 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

398

A. Nakane et al.

Table 8.84 Optical constants of a CuIn1−xGaxSe2-based compound [Cu/(In + Ga) = 0.69, x = 0.42] calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.887 2.893 2.901 2.911 2.921 2.930 2.936 2.939 2.939 2.938 2.937 2.938 2.945 2.958 2.978 3.003 3.034 3.068 3.101 3.134 3.166 3.223 3.261 3.271 3.259 3.235 3.205 3.175 3.147 3.120 3.096 3.074 3.055 3.039

1.118 1.101 1.084 1.067 1.047 1.027 1.006 0.986 0.968 0.956 0.949 0.947 0.950 0.954 0.957 0.958 0.955 0.944 0.927 0.906 0.879 0.811 0.725 0.634 0.553 0.487 0.435 0.394 0.362 0.337 0.316 0.299 0.286 0.274

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.024 3.011 3.000 2.989 2.980 2.972 2.966 2.960 2.954 2.950 2.946 2.943 2.940 2.938 2.936 2.935 2.933 2.932 2.931 2.929 2.927 2.926 2.924 2.922 2.919 2.916 2.913 2.910 2.906 2.901 2.896 2.891 2.886 2.881

0.264 0.255 0.247 0.239 0.233 0.226 0.220 0.215 0.209 0.204 0.199 0.193 0.188 0.182 0.176 0.17 0.163 0.156 0.149 0.142 0.135 0.127 0.119 0.111 0.103 9.55 × 8.74 × 7.94 × 7.15 × 6.38 × 5.64 × 4.94 × 4.28 × 3.62 ×

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.875 2.868 2.862 2.855 2.847 2.840 2.832 2.825 2.817 2.811 2.806 2.801 2.797 2.793 2.789 2.785 2.782 2.778 2.775 2.772 2.770 2.767 2.764 2.762 2.759 2.757 2.755 2.753 2.751 2.749 2.747 2.745 2.744

2.98 2.38 1.81 1.31 8.77 5.24 2.58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

× × × × × × ×

10−2 10−2 10−2 10−2 10−3 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

399

8.2.28 CuInGaSe2-Based Compound [Cu/(In + Ga) = 0.36] Data from S. Minoura, T. Maekawa, K. Kodera, A. Nakane, S. Niki and H. Fujiwara [30] (see also Fig. 10.9a in Vol. 1). The optical data of a low-Cu CuIn1−xGaxSe2-based polycrystalline layer [Cu/(In + Ga) = 0.36, x = 0.40] prepared by a single co-evaporation process at 520 °C are shown (Fig. 8.28, Tables 8.85 and 8.86).

Fig. 8.28 Dielectric function and absorption coefficient of a CuIn1−xGaxSe2-based compound [Cu/(In + Ga) = 0.36, x = 0.40] at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.85 Tauc-Lorentz parameters of (8.1) and (8.2) for a CuIn1−xGaxSe2-based compound [Cu/(In + Ga) = 0.36, x = 0.40]. The model parameters reported by S. Minoura et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

22.696 28.043 54.974 23.104 88.140

1.305 1.269 1.389 2.081 2.956

1.449 3.059 3.553 4.918 6.020

1.349 2.019 2.986 1.455 4.315

1.288 0 0 0 0

= = = = =

1 2 3 4 5

400

A. Nakane et al.

Table 8.86 Optical constants of a CuIn1−xGaxSe2-based compound [Cu/(In + Ga) = 0.36, x = 0.40] calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.796 2.810 2.825 2.839 2.853 2.867 2.880 2.893 2.905 2.916 2.926 2.934 2.942 2.949 2.957 2.964 2.972 2.979 2.987 2.995 3.003 3.015 3.023 3.026 3.021 3.010 2.993 2.974 2.953 2.932 2.911 2.891 2.872 2.855

1.180 1.149 1.120 1.092 1.066 1.039 1.012 0.986 0.959 0.933 0.907 0.881 0.857 0.834 0.812 0.790 0.768 0.747 0.725 0.702 0.679 0.630 0.580 0.528 0.476 0.429 0.386 0.349 0.318 0.292 0.270 0.251 0.237 0.224

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.839 2.825 2.812 2.801 2.791 2.783 2.776 2.770 2.766 2.763 2.760 2.758 2.757 2.755 2.754 2.752 2.751 2.749 2.748 2.746 2.743 2.740 2.737 2.733 2.729 2.725 2.720 2.714 2.708 2.702 2.695 2.689 2.682 2.674

0.214 0.206 0.199 0.193 0.188 0.184 0.180 0.176 0.173 0.169 0.164 0.159 0.154 0.148 0.141 0.135 0.128 0.120 0.113 0.105 9.69 × 8.88 × 8.08 × 7.27 × 6.48 × 5.71 × 4.96 × 4.24 × 3.56 × 2.93 × 2.34 × 1.81 × 1.35 × 9.41 ×

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.667 2.660 2.653 2.646 2.639 2.634 2.629 2.625 2.621 2.617 2.613 2.610 2.607 2.604 2.601 2.598 2.595 2.593 2.590 2.588 2.586 2.584 2.582 2.580 2.578 2.576 2.574 2.573 2.571 2.569 2.568 2.566 2.565

6.04 × 10−3 3.38 × 10−3 1.47 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3

8 Inorganic Semiconductors and Passivation Layers

401

8.2.29 Cu2ZnSnS4 Data from J. Li, H. Du, J. Yarbrough, A. Norman, K. Jones, G. Teeter, F. L. Terry Jr., and D. Levi [31]. The optical data of a polycrystalline Cu2ZnSnS4 layer (Cu:Zn: Sn = 1.94:1.06:1.01) prepared by a single co-evaporation process at 450 °C are shown.

Fig. 8.29 Dielectric function and absorption coefficient of Cu2ZnSnS4 at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.87 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnSnS4 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

10.562 32.722 36.534 195.722 103.461

1.013 2.448 1.303 2.801 0.885

1.540 2.790 4.055 4.674 5.994

1.009 1.548 2.967 3.683 5.823

1.730 0 0 0 0

= = = = =

1 2 3 4 5

Table 8.88 Optical constants of Cu2ZnSnS4 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335

2.869 2.873 2.870 2.862 2.848 2.830 2.809 2.789

0.878 0.832 0.788 0.746 0.708 0.676 0.651 0.633

540 550 560 570 580 590 600 610

2.837 2.836 2.834 2.832 2.830 2.827 2.824 2.822

0.405 0.390 0.376 0.364 0.353 0.342 0.333 0.325

λ (nm) 880 890 900 910 920 930 940 950

n

k

2.864 2.863 2.861 2.860 2.857 2.855 2.851 2.848

0.149 0.140 0.131 0.122 0.113 0.104 9.64 × 10−2 8.86 × 10−2 (continued)

402

A. Nakane et al.

Table 8.88 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.771 2.756 2.742 2.731 2.721 2.713 2.708 2.704 2.702 2.702 2.703 2.706 2.710 2.720 2.734 2.749 2.764 2.779 2.793 2.804 2.814 2.822 2.828 2.833 2.835 2.837

0.621 0.611 0.604 0.600 0.597 0.595 0.595 0.595 0.596 0.597 0.598 0.598 0.598 0.597 0.593 0.585 0.574 0.561 0.545 0.528 0.510 0.492 0.473 0.455 0.438 0.421

620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.819 2.817 2.816 2.815 2.815 2.815 2.816 2.817 2.819 2.821 2.824 2.827 2.830 2.834 2.837 2.841 2.844 2.848 2.851 2.854 2.857 2.859 2.861 2.863 2.864 2.864

0.318 0.312 0.306 0.301 0.296 0.292 0.288 0.284 0.280 0.275 0.271 0.266 0.261 0.255 0.249 0.242 0.236 0.229 0.221 0.213 0.205 0.196 0.187 0.178 0.168 0.159

960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.844 2.840 2.836 2.832 2.827 2.822 2.817 2.813 2.808 2.803 2.798 2.793 2.788 2.783 2.779 2.774 2.770 2.765 2.761 2.756 2.752 2.748 2.744 2.740 2.737

8.11 7.40 6.73 6.10 5.51 4.95 4.43 3.95 3.50 3.08 2.70 2.34 2.02 1.73 1.46 1.22 1.00 8.13 6.45 4.99 3.74 2.68 1.81 1.13 0

× × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3

8.2.30 Cu2ZnSnSe4 Data from Y. Hirate, H. Tampo, S. Minoura, H. Kadowaki, A. Nakane, K. M. Kim, H. Shibata, S. Niki and H. Fujiwara [32]. The optical data of a polycrystalline Cu2ZnSnSe4 layer (Cu:Zn:Sn:Se = 1.95:1.08:0.97:3.99) prepared by a single co-evaporation process at 370 °C are shown.

8 Inorganic Semiconductors and Passivation Layers

403

Fig. 8.30 Dielectric function and absorption coefficient of Cu2ZnSnSe4 at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.89 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnSnSe4. The model parameters reported by Hirate et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

11.122 25.139 63.399 173.079 231.270

1.330 1.664 1.563 2.205 2.009

1.177 2.401 3.789 4.549 5.886

0.700 1.150 2.598 3.566 5.455

0.770 0 0 0 0

= = = = =

1 2 3 4 5

Table 8.90 Optical constants of Cu2ZnSnSe4 calculated by the Tauc-Lorentz model λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355

2.895 2.911 2.925 2.938 2.949 2.956 2.959 2.958 2.954 2.946 2.936 2.924

1.239 1.200 1.162 1.123 1.083 1.043 1.003 0.965 0.928 0.894 0.863 0.834

λ (nm) 720 730 740 750 760 770 780 790 800 810 820 830

n

k

λ (nm)

n

k

3.086 3.082 3.079 3.075 3.072 3.069 3.066 3.063 3.061 3.058 3.056 3.055

0.414 0.403 0.393 0.383 0.374 0.366 0.359 0.352 0.345 0.339 0.333 0.327

1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350

3.056 3.055 3.054 3.053 3.051 3.050 3.048 3.047 3.045 3.043 3.041 3.039

0.134 0.129 0.124 0.119 0.114 0.11 0.105 0.101 9.61 × 10−2 9.17 × 10−2 8.75 × 10−2 8.33 × 10−2 (continued)

404

A. Nakane et al.

Table 8.90 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

2.910 2.894 2.876 2.858 2.839 2.821 2.803 2.788 2.773 2.751 2.737 2.732 2.736 2.748 2.766 2.790 2.819 2.850 2.883 2.914 2.945 2.973 2.998 3.021 3.040 3.057 3.070 3.081 3.090 3.096 3.100 3.103 3.104 3.104 3.103 3.101 3.099 3.096 3.093 3.089

0.807 0.785 0.765 0.750 0.738 0.730 0.726 0.724 0.725 0.734 0.749 0.767 0.786 0.805 0.821 0.833 0.841 0.842 0.838 0.829 0.815 0.798 0.777 0.755 0.731 0.706 0.680 0.655 0.630 0.606 0.583 0.561 0.539 0.520 0.501 0.484 0.467 0.452 0.439 0.426

840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230

3.053 3.052 3.051 3.050 3.049 3.049 3.049 3.048 3.048 3.049 3.049 3.049 3.049 3.050 3.050 3.051 3.051 3.052 3.053 3.053 3.054 3.054 3.055 3.055 3.056 3.057 3.057 3.058 3.058 3.059 3.059 3.059 3.059 3.059 3.059 3.059 3.059 3.058 3.057 3.057

0.322 0.317 0.312 0.307 0.303 0.298 0.294 0.289 0.285 0.280 0.276 0.272 0.267 0.263 0.258 0.254 0.249 0.245 0.240 0.236 0.231 0.227 0.222 0.218 0.213 0.209 0.204 0.199 0.194 0.189 0.184 0.179 0.174 0.169 0.164 0.159 0.154 0.149 0.144 0.139

1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730

3.037 3.035 3.033 3.031 3.028 3.026 3.023 3.021 3.018 3.016 3.013 3.011 3.008 3.005 3.003 3.000 2.997 2.994 2.992 2.989 2.986 2.983 2.980 2.978 2.975 2.972 2.969 2.967 2.964 2.961 2.959 2.956 2.954 2.951 2.949 2.946 2.944 2.941

7.92 7.53 7.14 6.76 6.39 6.04 5.69 5.36 5.03 4.72 4.41 4.12 3.84 3.56 3.30 3.05 2.81 2.58 2.36 2.15 1.95 1.77 1.59 1.42 1.26 1.11 9.76 8.47 7.28 6.18 5.18 4.27 3.45 2.72 2.08 1.53 1.07 0

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

8 Inorganic Semiconductors and Passivation Layers

405

8.2.31 Cu2ZnSn(SxSe1−x)4 The dielectric functions of Cu2ZnSn(SxSe1−x)4 with different S composition of x = S/(S + Se) are summarized. These dielectric functions were obtained from an Cu2ZnSn(SxSe1−x)4 optical database (A. Nakane, H. Tampo, M. Tamakoshi, S. Fujimoto, K. M. Kim, S. Kim, H. Shibata, S. Niki and H. Fujiwara [33]), in which the Cu2ZnSn(S,Se)4 optical constants for arbitrary S content are deduced by applying the energy shift model (Sect. 10.4.1 in Vol. 1). Based on this method, various Cu2ZnSn(S,Se)4 dielectric functions (x = 0.2–0.8) with a constant Cu composition [Cu/(Zn + Sn) ∼ 0.95] were calculated using the dielectric functions of Cu2ZnSnS4 (Fig. 8.29) and Cu2ZnSnSe4 (Fig. 8.30). The dielectric functions obtained from this procedure have been parameterized further using the Tauc-Lorentz model and the modeled results are described here. The Tauc-Lorentz parameters and optical constants of x = 0.0 (Cu2ZnSnSe4) and x = 1.0 (Cu2ZnSnS4) are shown in Tables 8.87, 8.88, 8.89 and 8.90 (Fig. 8.31, Tables 8.91, 8.92, 8.93, 8.94, 8.95, 8.96, 8.97 and 8.98).

Fig. 8.31 Dielectric functions, optical constants and absorption coefficients of various Cu2ZnSn (SxSe1−x)4 calculated by the Tauc-Lorentz model [(8.1) and (8.2)]. The Cu2ZnSn(SxSe1−x)4 dielectric functions in a range of x = 0.2–0.8 represent those calculated from the energy shift model, whereas the dielectric functions of x = 0.0 and x = 1.0 correspond to those shown in Figs. 8.30 and 8.29, respectively

406

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Table 8.91 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnSn(SxSe1−x)4 (x = 0.2) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

11.278 25.951 57.917 181.771 205.806

1.265 1.728 1.499 2.271 1.942

1.245 2.467 3.852 4.582 5.906

0.762 1.229 2.653 3.614 5.515

0.979 0 0 0 0

= = = = =

1 2 3 4 5

Table 8.92 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnSn(SxSe1−x)4 (x = 0.4) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

11.031 26.614 55.577 158.392 194.914

1.179 1.825 1.521 2.463 1.862

1.313 2.542 3.872 4.683 5.881

0.823 1.295 2.740 3.532 5.575

1.184 0 0 0 0

= = = = =

1 2 3 4 5

Table 8.93 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnSn(SxSe1−x)4 (x = 0.6) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

11.010 27.995 49.458 162.760 185.419

1.132 1.941 1.481 2.580 1.631

1.391 2.612 3.934 4.718 5.824

0.884 1.384 2.799 3.560 5.656

1.374 0 0 0 0

= = = = =

1 2 3 4 5

Table 8.94 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnSn(SxSe1−x)4 (x = 0.8) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

10.868 29.936 42.757 177.685 167.614

1.080 2.123 1.401 2.689 1.240

1.467 2.690 3.997 4.710 5.817

0.946 1.471 2.867 3.620 5.750

1.558 0 0 0 0

= = = = =

1 2 3 4 5

8 Inorganic Semiconductors and Passivation Layers

407

Table 8.95 Optical constants of Cu2ZnSn(SxSe1−x)4 (x = 0.2) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570

2.893 2.908 2.922 2.933 2.940 2.943 2.942 2.936 2.926 2.914 2.901 2.886 2.869 2.851 2.832 2.814 2.797 2.781 2.766 2.754 2.744 2.730 2.725 2.729 2.741 2.758 2.781 2.808 2.838 2.868 2.897 2.924 2.949 2.971 2.991 3.007 3.020 3.031

1.170 1.130 1.091 1.050 1.008 0.967 0.927 0.889 0.854 0.824 0.796 0.771 0.749 0.732 0.718 0.708 0.702 0.699 0.699 0.701 0.705 0.718 0.734 0.750 0.766 0.779 0.788 0.793 0.792 0.785 0.774 0.758 0.740 0.719 0.696 0.672 0.647 0.623

670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040

3.043 3.039 3.036 3.032 3.029 3.025 3.022 3.019 3.017 3.014 3.012 3.010 3.009 3.007 3.006 3.006 3.005 3.005 3.005 3.005 3.005 3.006 3.006 3.007 3.008 3.008 3.009 3.010 3.011 3.012 3.013 3.014 3.015 3.015 3.016 3.017 3.018 3.019

0.427 0.414 0.402 0.391 0.381 0.372 0.363 0.355 0.348 0.341 0.335 0.329 0.323 0.318 0.313 0.308 0.303 0.298 0.293 0.289 0.284 0.279 0.275 0.270 0.265 0.260 0.256 0.251 0.246 0.241 0.236 0.231 0.226 0.221 0.215 0.210 0.205 0.199

1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510

3.019 3.018 3.017 3.015 3.014 3.012 3.011 3.009 3.007 3.005 3.003 3.000 2.998 2.995 2.993 2.990 2.987 2.985 2.982 2.979 2.976 2.973 2.970 2.967 2.964 2.960 2.957 2.954 2.951 2.948 2.945 2.941 2.938 2.935 2.932 2.929 2.926 2.923

0.141 0.136 0.130 0.124 0.119 0.114 0.108 0.103 9.78 × 10−2 9.28 × 10−2 8.80 × 10−2 8.32 × 10−2 7.86 × 10−2 7.41 × 10−2 6.97 × 10−2 6.55 × 10−2 6.14 × 10−2 5.75 × 10−2 5.36 × 10−2 5.00 × 10−2 4.64 × 10−2 4.30 × 10−2 3.98 × 10−2 3.67 × 10−2 3.37 × 10−2 3.08 × 10−2 2.81 × 10−2 2.56 × 10−2 2.31 × 10−2 2.08 × 10−2 1.87 × 10−2 1.66 × 10−2 1.47 × 10−2 1.29 × 10−2 1.13 × 10−2 9.72 × 10−3 8.30 × 10−3 7.00 × 10−3 (continued)

408

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Table 8.95 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

580 590 600 610 620 630 640 650 660

3.039 3.045 3.049 3.051 3.052 3.052 3.050 3.048 3.046

0.598 0.575 0.552 0.531 0.510 0.491 0.473 0.457 0.441

1050 1060 1070 1080 1090 1100 1110 1120 1130

3.020 3.020 3.021 3.021 3.021 3.021 3.021 3.020 3.020

0.194 0.188 0.182 0.176 0.171 0.165 0.159 0.153 0.147

1520 1530 1540 1550 1560 1570 1580 1590

2.920 2.917 2.914 2.911 2.908 2.905 2.903 2.900

5.82 4.75 3.80 2.96 2.23 1.60 1.08 0

× × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3

Table 8.96 Optical constants of Cu2ZnSn(SxSe1−x)4 (x = 0.4) calculated by the Tauc-Lorentz model λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420

2.889 2.903 2.914 2.921 2.925 2.924 2.918 2.908 2.894 2.877 2.859 2.841 2.824 2.807 2.790 2.775 2.761 2.749 2.738 2.730 2.724 2.719 2.722

1.099 1.058 1.017 0.975 0.933 0.892 0.853 0.816 0.784 0.757 0.734 0.716 0.701 0.690 0.682 0.677 0.675 0.675 0.677 0.681 0.687 0.699 0.713

λ (nm) 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850

n

k

λ (nm)

n

k

2.996 2.993 2.990 2.986 2.983 2.980 2.976 2.973 2.971 2.968 2.966 2.964 2.963 2.961 2.961 2.960 2.960 2.960 2.960 2.961 2.962 2.963 2.964

0.432 0.417 0.404 0.392 0.381 0.371 0.361 0.353 0.345 0.338 0.332 0.325 0.320 0.314 0.309 0.304 0.299 0.295 0.290 0.285 0.280 0.275 0.270

1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280

2.981 2.980 2.979 2.978 2.976 2.974 2.972 2.970 2.968 2.965 2.963 2.960 2.957 2.954 2.951 2.948 2.945 2.941 2.938 2.934 2.931 2.927 2.924

0.145 0.139 0.132 0.126 0.119 0.113 0.107 0.101 9.56 × 10−2 9.00 × 10−2 8.46 × 10−2 7.93 × 10−2 7.43 × 10−2 6.93 × 10−2 6.46 × 10−2 6.01 × 10−2 5.57 × 10−2 5.15 × 10−2 4.75 × 10−2 4.37 × 10−2 4.00 × 10−2 3.66 × 10−2 3.33 × 10−2 (continued)

8 Inorganic Semiconductors and Passivation Layers

409

Table 8.96 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620

2.733 2.749 2.771 2.796 2.823 2.851 2.876 2.900 2.922 2.940 2.956 2.969 2.980 2.988 2.994 2.997 2.999 3.000 2.999 2.998

0.726 0.736 0.742 0.744 0.740 0.731 0.718 0.701 0.682 0.661 0.638 0.615 0.591 0.568 0.545 0.523 0.503 0.483 0.465 0.448

860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050

2.965 2.967 2.968 2.969 2.971 2.972 2.973 2.975 2.976 2.977 2.978 2.979 2.980 2.981 2.982 2.982 2.982 2.982 2.982 2.982

0.265 0.260 0.255 0.250 0.244 0.239 0.233 0.227 0.222 0.216 0.210 0.204 0.198 0.191 0.185 0.178 0.172 0.165 0.158 0.152

1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470

2.920 2.917 2.913 2.910 2.906 2.902 2.899 2.895 2.892 2.888 2.885 2.882 2.878 2.875 2.872 2.869 2.865 2.862 2.860

3.02 2.72 2.44 2.18 1.94 1.71 1.50 1.30 1.12 9.54 8.02 6.64 5.41 4.31 3.34 2.50 1.79 1.20 0

× × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

Table 8.97 Optical constants of Cu2ZnSn(SxSe1−x)4 (x = 0.6) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370

2.886 2.897 2.905 2.908 2.906 2.899 2.888 2.873 2.855 2.836 2.817 2.800 2.784 2.769 2.755

1.027 0.984 0.941 0.898 0.856 0.816 0.779 0.747 0.720 0.699 0.683 0.670 0.660 0.654 0.650

600 610 620 630 640 650 660 670 680 690 700 710 720 730 740

2.944 2.941 2.938 2.935 2.932 2.929 2.926 2.923 2.920 2.918 2.916 2.915 2.914 2.913 2.913

0.423 0.408 0.394 0.382 0.371 0.361 0.352 0.343 0.336 0.329 0.323 0.317 0.312 0.306 0.302

1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140

2.942 2.940 2.939 2.937 2.935 2.933 2.930 2.928 2.925 2.922 2.919 2.915 2.912 2.908 2.905

0.141 0.134 0.127 0.120 0.113 0.106 9.95 × 10−2 9.31 × 10−2 8.69 × 10−2 8.10 × 10−2 7.53 × 10−2 6.98 × 10−2 6.45 × 10−2 5.95 × 10−2 5.46 × 10−2 (continued)

410

A. Nakane et al.

Table 8.97 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590

2.743 2.733 2.725 2.719 2.715 2.714 2.716 2.725 2.740 2.759 2.782 2.806 2.829 2.851 2.871 2.889 2.904 2.917 2.927 2.935 2.940 2.944 2.945 2.946 2.945

0.649 0.649 0.651 0.655 0.659 0.664 0.674 0.683 0.689 0.692 0.691 0.685 0.675 0.660 0.643 0.624 0.603 0.581 0.559 0.537 0.515 0.495 0.475 0.456 0.439

750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990

2.913 2.913 2.914 2.915 2.917 2.918 2.920 2.922 2.924 2.926 2.928 2.930 2.932 2.933 2.935 2.937 2.938 2.940 2.941 2.942 2.943 2.943 2.943 2.943 2.942

0.297 0.292 0.287 0.283 0.278 0.273 0.268 0.262 0.257 0.251 0.246 0.240 0.234 0.227 0.221 0.215 0.208 0.201 0.194 0.186 0.179 0.171 0.164 0.156 0.149

1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370

2.901 2.897 2.893 2.889 2.885 2.881 2.877 2.873 2.869 2.865 2.861 2.857 2.853 2.850 2.846 2.842 2.838 2.835 2.831 2.828 2.824 2.821 2.818

5.01 4.57 4.16 3.77 3.40 3.06 2.73 2.43 2.15 1.88 1.64 1.42 1.21 1.02 8.54 7.01 5.65 4.44 3.39 2.49 1.74 1.13 0

× × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

Table 8.98 Optical constants of Cu2ZnSn(SxSe1−x)4 (x = 0.8) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340

2.879 2.887 2.890 2.888 2.880 2.868 2.851 2.832 2.812

0.953 0.909 0.865 0.822 0.781 0.744 0.712 0.686 0.666

570 580 590 600 610 620 630 640 650

2.891 2.890 2.887 2.885 2.882 2.879 2.876 2.873 2.870

0.414 0.399 0.385 0.373 0.361 0.351 0.342 0.334 0.327

940 950 960 970 980 990 1000 1010 1020

2.902 2.901 2.900 2.898 2.895 2.893 2.890 2.887 2.883

0.142 0.134 0.126 0.118 0.110 0.103 9.56 × 10−2 8.86 × 10−2 8.19 × 10−2 (continued)

8 Inorganic Semiconductors and Passivation Layers

411

Table 8.98 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560

2.794 2.777 2.762 2.749 2.737 2.727 2.719 2.713 2.710 2.708 2.708 2.710 2.718 2.731 2.747 2.766 2.786 2.806 2.824 2.840 2.854 2.865 2.875 2.882 2.887 2.890 2.892 2.892

0.651 0.640 0.632 0.627 0.624 0.623 0.623 0.625 0.627 0.630 0.633 0.636 0.641 0.643 0.643 0.639 0.630 0.618 0.603 0.586 0.567 0.547 0.526 0.506 0.486 0.466 0.448 0.430

660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930

2.868 2.867 2.865 2.865 2.865 2.865 2.865 2.867 2.868 2.870 2.872 2.875 2.877 2.880 2.882 2.885 2.888 2.890 2.892 2.895 2.897 2.899 2.901 2.902 2.903 2.904 2.904 2.903

0.320 0.314 0.309 0.303 0.299 0.294 0.290 0.285 0.280 0.276 0.271 0.266 0.260 0.255 0.249 0.243 0.236 0.230 0.223 0.216 0.208 0.201 0.193 0.184 0.176 0.168 0.159 0.151

1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280

2.880 2.876 2.872 2.868 2.864 2.860 2.855 2.851 2.847 2.842 2.838 2.833 2.829 2.824 2.820 2.816 2.812 2.807 2.803 2.799 2.795 2.792 2.788 2.784 2.781 2.777

7.55 6.94 6.36 5.81 5.29 4.79 4.33 3.89 3.48 3.10 2.74 2.41 2.11 1.83 1.57 1.34 1.12 9.32 7.60 6.08 4.74 3.59 2.61 1.79 1.14 0

× × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

8.2.32 Cu2ZnGeSe4 Data: unpublished results of S. Fujimoto, S. Kim and H. Tampo. The optical data of a polycrystalline Cu2ZnGeSe4 layer (Cu:Zn:Ge:Se = 2.00:1.11:0.96:3.93), prepared by a single co-evaporation process at a low temperature (200 °C) and the following thermal annealing at 500–550 °C under GeSe2 + Se atmosphere, are shown. The preparation and characterization results are described in [34] (Fig. 8.32, Tables 8.99 and 8.100).

412

A. Nakane et al.

Fig. 8.32 Dielectric function and absorption coefficient of Cu2ZnGeSe4 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.99 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2ZnGeSe4 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j

9.595 20.178 8.758 28.586 0.724 54.292 0.350 91.874 204.022 647.965

0.256 0.892 0.216 1.056 0.253 1.310 0.321 2.053 1.204 0.040

1.418 1.556 1.593 2.535 3.400 3.995 4.736 5.140 6.253 6.759

1.296 1.358 1.586 1.583 2.032 2.585 1.998 3.309 5.506 6.577

1.319 0 0 0 0 0 0 0 0 0

= = = = = = = = = =

1 2 3 4 5 6 7 8 9 10

Table 8.100 Optical constants of Cu2ZnGeSe4. The optical data obtained by S. Fujimoto, S. Kim and H. Tampo are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350

3.030 3.070 3.104 3.130 3.149 3.158 3.154 3.135 3.105 3.072 3.047

1.257 1.211 1.159 1.103 1.041 0.977 0.911 0.851 0.803 0.767 0.743

540 550 560 570 580 590 600 610 620 630 640

3.217 3.214 3.209 3.199 3.189 3.178 3.166 3.157 3.146 3.138 3.130

0.533 0.491 0.455 0.423 0.394 0.370 0.351 0.332 0.317 0.304 0.288

λ (nm) 880 890 900 910 920 930 940 950 960 970 980

n

k

3.047 3.036 3.025 3.012 3.000 2.989 2.979 2.969 2.959 2.951 2.943

4.44 × 10−2 3.13 × 10−2 2.06 × 10−2 1.34 × 10−2 7.63 × 10−3 2.52 × 10−3 0 0 0 0 0 (continued)

8 Inorganic Semiconductors and Passivation Layers

413

Table 8.100 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.021 3.007 3.002 2.993 2.965 2.935 2.917 2.892 2.872 2.856 2.828 2.820 2.834 2.865 2.911 2.959 3.005 3.055 3.105 3.148 3.179 3.201 3.210

0.729 0.719 0.703 0.678 0.658 0.652 0.644 0.646 0.651 0.661 0.690 0.727 0.760 0.791 0.808 0.807 0.802 0.791 0.761 0.721 0.676 0.627 0.580

650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.122 3.115 3.112 3.106 3.103 3.100 3.098 3.096 3.095 3.095 3.090 3.086 3.081 3.076 3.073 3.068 3.065 3.065 3.065 3.064 3.062 3.059 3.054

0.278 0.268 0.257 0.247 0.240 0.228 0.220 0.212 0.201 0.189 0.176 0.167 0.157 0.148 0.139 0.133 0.124 0.118 0.107 9.82 × 8.46 × 7.27 × 5.94 ×

990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.936 2.929 2.924 2.920 2.914 2.909 2.903 2.900 2.895 2.892 2.889 2.886 2.882 2.879 2.876 2.873 2.871 2.868 2.867 2.863 2.862 2.859

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2

8.2.33 Cu2SnSe3 Two optical data sets extracted from cubic and monoclinic Cu2SnSe3 polycrystals are summarized: (i) Cubic Cu2SnSe3: Y. Hirate, H. Tampo, S. Minoura, H. Kadowaki, A. Nakane, K. M. Kim, H. Shibata, S. Niki and H. Fujiwara [32]. (ii) Monoclinic Cu2SnSe3: S. G. Choi, J. Kang, J. Li, H. Haneef, N. J. Podraza, C. Beall, S.-H. Wei, S. T. Christensen and I. L. Repins [35]. The optical data have been extracted from Cu2SnSe3 layers prepared by a single co-evaporation process at 370 °C (cubic) and 455 °C (monoclinic), and the composition of the cubic phase is Cu:Sn:Se = 2.06:0.99:2.95. The optical functions parameterized by the Tauc-Lorentz model are summarized. For the dielectric function of the cubic phase, the contribution of the free carrier absorption has been removed based on the analysis using the Drude model (Fig. 8.33, Tables 8.101, 8.102, 8.103 and 8.104).

414

A. Nakane et al.

Fig. 8.33 Dielectric functions and absorptions coefficient of Cu2SnSe3 at room temperature. The solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.101 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2SnSe3 (cubic). The model parameters reported by Hirate et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

5.268 7.194 28.799 89.533 49.140 93.356

1.084 1.491 1.467 4.499 1.508 0.544

0.684 1.768 2.257 3.216 3.917 4.333

0.387 0.411 1.249 1.908 2.517 4.093

1.294 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

Table 8.102 Tauc-Lorentz parameters of (8.1) and (8.2) for Cu2SnSe3 (monoclinic). The model parameters reported by Choi et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

2.84 0.94 9.41 1.55 3.21 1.84 7.16 16.06 33.09

0.06 0.12 1.13 0.53 0.90 0.57 2.12 2.56 5.12

0.49 0.58 0.75 1.57 2.10 2.44 4.20 5.21 8.23

0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46

1.0 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

8 Inorganic Semiconductors and Passivation Layers

415

Table 8.103 Optical constants of Cu2SnSe3 (cubic) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580

2.605 2.663 2.721 2.774 2.820 2.858 2.889 2.911 2.927 2.937 2.943 2.944 2.944 2.941 2.937 2.933 2.929 2.925 2.921 2.918 2.916 2.914 2.917 2.923 2.933 2.948 2.965 2.986 3.010 3.035 3.063 3.091 3.119 3.145 3.170 3.193 3.213 3.231 3.246

1.869 1.845 1.809 1.766 1.718 1.666 1.614 1.562 1.512 1.466 1.423 1.385 1.351 1.320 1.294 1.271 1.251 1.235 1.220 1.208 1.198 1.182 1.172 1.164 1.159 1.155 1.151 1.146 1.140 1.132 1.122 1.108 1.091 1.071 1.049 1.025 1.000 0.974 0.947

750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

3.323 3.324 3.324 3.324 3.323 3.323 3.322 3.321 3.319 3.318 3.316 3.314 3.312 3.310 3.307 3.305 3.303 3.300 3.297 3.295 3.292 3.290 3.288 3.285 3.283 3.282 3.280 3.278 3.277 3.276 3.275 3.273 3.272 3.271 3.270 3.269 3.268 3.267 3.267

0.620 0.605 0.592 0.578 0.565 0.553 0.541 0.529 0.518 0.507 0.496 0.486 0.477 0.467 0.459 0.450 0.442 0.435 0.428 0.421 0.415 0.408 0.403 0.398 0.393 0.388 0.383 0.379 0.374 0.370 0.366 0.362 0.358 0.354 0.350 0.346 0.343 0.339 0.336

1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2050 2100 2150 2200 2250 2300 2350 2400

3.261 3.262 3.263 3.263 3.264 3.265 3.266 3.267 3.268 3.269 3.270 3.271 3.272 3.273 3.274 3.274 3.275 3.276 3.277 3.277 3.278 3.279 3.279 3.279 3.280 3.280 3.280 3.280 3.280 3.280 3.280 3.280 3.278 3.277 3.274 3.272 3.269 3.265 3.262

0.267 0.263 0.258 0.254 0.250 0.246 0.242 0.237 0.233 0.229 0.225 0.220 0.216 0.212 0.208 0.203 0.199 0.194 0.190 0.186 0.181 0.177 0.173 0.168 0.164 0.160 0.155 0.151 0.147 0.142 0.138 0.127 0.117 0.107 9.73 × 10−2 8.79 × 10−2 7.89 × 10−2 7.03 × 10−2 6.22 × 10−2 (continued)

416

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Table 8.103 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740

3.259 3.269 3.278 3.284 3.290 3.294 3.298 3.302 3.306 3.309 3.313 3.315 3.318 3.319 3.321 3.322

0.921 0.895 0.870 0.847 0.824 0.804 0.785 0.766 0.748 0.731 0.713 0.697 0.680 0.664 0.649 0.634

1140 1150 1160 1170 1180 1190 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380

3.266 3.265 3.264 3.264 3.263 3.263 3.262 3.261 3.261 3.260 3.260 3.260 3.260 3.260 3.260 3.261

0.333 0.330 0.326 0.323 0.320 0.318 0.315 0.309 0.304 0.299 0.294 0.289 0.285 0.280 0.276 0.271

2450 2500 2550 2600 2650 2700 2750 2800 2850 2900 2950 3000 3050 3100

3.257 3.253 3.248 3.243 3.238 3.233 3.228 3.222 3.217 3.211 3.206 3.201 3.196 3.191

5.45 4.73 4.06 3.44 2.87 2.35 1.89 1.48 1.12 8.10 5.56 3.53 2.00 0

× × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3

Table 8.104 Optical constants of Cu2SnSe3 (monoclinic) calculated by the Tauc-Lorentz model λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380

3.096 3.110 3.120 3.128 3.132 3.135 3.134 3.131 3.127 3.120 3.112 3.102 3.092 3.080 3.067 3.054 3.040

1.256 1.216 1.176 1.138 1.100 1.064 1.029 0.996 0.965 0.936 0.909 0.884 0.861 0.841 0.822 0.805 0.790

λ (nm) 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880

n

k

λ (nm)

n

k

3.273 3.278 3.284 3.292 3.302 3.312 3.323 3.334 3.345 3.355 3.363 3.371 3.377 3.381 3.384 3.386 3.387

0.652 0.649 0.646 0.643 0.638 0.633 0.626 0.617 0.607 0.596 0.583 0.569 0.555 0.541 0.527 0.514 0.501

1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600

3.353 3.356 3.358 3.360 3.363 3.366 3.368 3.371 3.374 3.376 3.379 3.381 3.384 3.386 3.388 3.390 3.392

0.327 0.323 0.319 0.315 0.311 0.307 0.303 0.298 0.294 0.289 0.285 0.280 0.275 0.270 0.265 0.260 0.255 (continued)

8 Inorganic Semiconductors and Passivation Layers

417

Table 8.104 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

3.026 3.012 2.997 2.982 2.953 2.924 2.898 2.875 2.858 2.850 2.856 2.877 2.915 2.965 3.019 3.069 3.110 3.141 3.163 3.181 3.195 3.208 3.220 3.231 3.241 3.249 3.255 3.260 3.263 3.265 3.266 3.266 3.267 3.268 3.270

0.778 0.767 0.758 0.752 0.744 0.745 0.754 0.771 0.798 0.833 0.874 0.915 0.951 0.972 0.977 0.965 0.944 0.918 0.893 0.870 0.850 0.831 0.812 0.795 0.777 0.759 0.742 0.726 0.711 0.697 0.685 0.675 0.667 0.661 0.656

890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1220 1240 1260

3.387 3.386 3.385 3.383 3.381 3.378 3.376 3.373 3.371 3.368 3.366 3.363 3.361 3.359 3.357 3.355 3.354 3.352 3.351 3.350 3.349 3.348 3.347 3.347 3.346 3.346 3.346 3.346 3.346 3.346 3.347 3.347 3.348 3.350 3.351

0.488 0.477 0.466 0.456 0.447 0.438 0.430 0.423 0.416 0.410 0.404 0.399 0.394 0.390 0.386 0.382 0.378 0.375 0.372 0.369 0.366 0.364 0.361 0.359 0.356 0.354 0.352 0.350 0.348 0.346 0.344 0.342 0.338 0.335 0.331

1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650 2700

3.394 3.395 3.397 3.398 3.399 3.400 3.401 3.402 3.403 3.403 3.404 3.404 3.405 3.405 3.406 3.407 3.408 3.409 3.411 3.413 3.420 3.428 3.434 3.436 3.433 3.428 3.423 3.420 3.420 3.420 3.414 3.399 3.382 3.368

0.250 0.245 0.240 0.235 0.230 0.226 0.221 0.216 0.212 0.208 0.204 0.200 0.196 0.193 0.189 0.186 0.183 0.181 0.178 0.175 0.167 0.155 0.139 0.121 0.104 8.98 × 7.91 × 7.02 × 5.99 × 4.46 × 2.53 × 9.72 × 1.81 × 0

10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

418

A. Nakane et al.

8.2.34 In2S3 Data from S. Marsillac, N. Barreau, H. Khatri, J. Li, D. Sainju, A. Parikh, N. J. Podraza and R. W. Collins [36]. The optical data of a polycrystalline In2S3 layer prepared by co-evaporation at 200 °C are shown (Fig. 8.34, Tables 8.105 and 8.106).

Fig. 8.34 Dielectric function and absorption coefficient of In2S3 at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)] Table 8.105 Tauc-Lorentz parameters of (8.1) and (8.2) for In2S3 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

8.470 63.324 13.276 142.697 14.782 47.434

0.890 1.467 0.681 3.045 0.777 0.481

2.359 3.014 3.735 4.869 4.899 5.584

1.950 2.394 3.155 3.145 3.156 4.868

1.570 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

Table 8.106 Optical constants of In2S3. The optical data obtained by S. Marsillac are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335

3.140 3.131 3.124 3.116 3.104 3.111 3.112 3.099

0.837 0.803 0.773 0.746 0.720 0.691 0.670 0.633

540 550 560 570 580 590 600 610

2.820 2.804 2.788 2.771 2.757 2.743 2.732 2.720

3.88 3.08 2.34 1.58 1.09 8.25 5.01 1.72

λ (nm) × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3

880 890 900 910 920 930 940 950

n

k

2.589 0 2.587 0 2.585 0 2.582 0 2.580 0 2.578 0 2.575 0 2.573 0 (continued)

8 Inorganic Semiconductors and Passivation Layers

419

Table 8.106 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.091 3.092 3.083 3.075 3.069 3.063 3.059 3.057 3.056 3.058 3.061 3.062 3.065 3.069 3.070 3.067 3.053 3.035 3.008 2.979 2.948 2.919 2.893 2.872 2.853 2.837

0.606 0.585 0.565 0.547 0.530 0.513 0.497 0.481 0.468 0.451 0.434 0.416 0.399 0.363 0.320 0.268 0.221 0.182 0.154 0.127 0.106 8.84 × 7.47 × 6.36 × 5.42 × 4.67 ×

620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.709 2.699 2.690 2.681 2.672 2.666 2.660 2.654 2.648 2.643 2.639 2.634 2.630 2.625 2.622 2.618 2.615 2.612 2.608 2.605 2.603 2.600 2.598 2.596 2.594 2.592

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.571 2.570 2.567 2.566 2.564 2.562 2.561 2.559 2.557 2.556 2.554 2.553 2.553 2.552 2.551 2.550 2.549 2.549 2.548 2.547 2.547 2.546 2.546 2.545 2.545

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2

8.2.35 MoS2 Data from A. R. Beal and H. P. Hughes [37]. The optical data of a MoS2 single crystal are shown (Fig. 8.35, Tables 8.107 and 8.108).

420

A. Nakane et al.

Fig. 8.35 Dielectric function and absorption coefficient of MoS2 (single crystal) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.107 Tauc-Lorentz parameters of (8.1) and (8.2) for MoS2 (single crystal) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

82.008 193.604 106.419 315.846 175.565 91.133 57.615 562.577

0.105 0.095 0.163 0.314 0.490 0.437 0.820 1.142

1.729 1.824 2.007 2.101 2.655 3.043 3.844 4.132

1.630 1.688 1.760 2.057 1.962 2.424 2.732 3.798

1.770 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 8.108 Optical constants of MoS2 (single crystal) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340

3.052 3.037 3.021 3.010 3.002 2.995 2.986 2.963 2.925

2.321 2.287 2.270 2.264 2.261 2.260 2.258 2.257 2.272

540 550 560 570 580 590 600 610 620

5.101 5.009 4.928 4.845 4.753 4.680 4.716 4.945 5.196

1.096 1.062 1.040 1.033 1.062 1.165 1.344 1.453 1.314

λ (nm) 880 890 900 910 920 930 940 950 960

n

k

4.527 0 4.508 0 4.490 0 4.474 0 4.458 0 4.443 0 4.429 0 4.416 0 4.403 0 (continued)

8 Inorganic Semiconductors and Passivation Layers

421

Table 8.108 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.883 2.845 2.819 2.811 2.825 2.865 2.932 3.028 3.154 3.306 3.476 3.651 3.941 4.113 4.267 4.516 4.871 5.258 5.565 5.717 5.717 5.622 5.484 5.342 5.212

2.310 2.372 2.457 2.560 2.676 2.800 2.926 3.048 3.157 3.243 3.297 3.311 3.243 3.168 3.182 3.231 3.206 3.027 2.694 2.288 1.906 1.602 1.385 1.242 1.151

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

5.234 5.104 4.959 4.928 5.175 5.640 5.747 5.584 5.471 5.408 5.293 5.158 5.046 4.958 4.891 4.836 4.788 4.746 4.709 4.676 4.646 4.618 4.593 4.569 4.547

1.059 0.919 0.950 1.133 1.344 1.188 0.716 0.449 0.340 0.217 9.15 × 10−2 2.77 × 10−2 4.97 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0

970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

4.391 4.380 4.369 4.358 4.349 4.339 4.330 4.321 4.313 4.305 4.297 4.290 4.283 4.276 4.270 4.263 4.257 4.251 4.246 4.240 4.235 4.230 4.225 4.220

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8.2.36 MoSe2 (Polycrystal) Data from M. Richter, C. Schubbert, P. Eraerds, I. Riedel, J. Keller, J. Parisi, T. Dalibor, and A. Avellan-Hampe [38]. The optical data have been extracted from a MoSe2 layer formed by selenization of a Mo layer during rapid thermal processing (Tables 8.109 and 8.110).

422

A. Nakane et al.

Fig. 8.36 Dielectric function and absorption coefficient of MoSe2 (polycrystal) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 8.109 Tauc-Lorentz parameters of (8.1) and (8.2) for MoSe2 (polycrystal) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

22.010 103.004 1.676 9.249

0.855 3.880 5.317 1.646

1.915 2.281 2.910 2.936

1.250 2.276 0.107 1.002

1.448 0 0 0

= = = =

1 2 3 4

Table 8.110 Optical constants of MoSe2 (polycrystal) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380

1.544 1.566 1.590 1.613 1.637 1.661 1.686 1.711 1.737 1.763 1.789 1.816 1.844 1.871 1.900 1.928 1.956

1.091 1.101 1.111 1.120 1.129 1.137 1.145 1.152 1.159 1.165 1.170 1.174 1.177 1.179 1.180 1.180 1.178

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700

2.393 2.416 2.443 2.475 2.510 2.547 2.585 2.624 2.661 2.696 2.728 2.756 2.780 2.798 2.812 2.820 2.824

0.897 0.899 0.900 0.898 0.893 0.883 0.868 0.848 0.823 0.793 0.759 0.721 0.680 0.638 0.595 0.552 0.510

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040

2.617 2.604 2.592 2.581 2.570 2.559 2.549 2.539 2.530 2.521 2.513 2.506 2.499 2.493 2.487 2.481 2.476

0.110 0.103 9.63 × 10−2 9.07 × 10−2 8.58 × 10−2 8.16 × 10−2 7.79 × 10−2 7.48 × 10−2 7.23 × 10−2 7.02 × 10−2 6.85 × 10−2 6.72 × 10−2 6.62 × 10−2 6.52 × 10−2 6.43 × 10−2 6.34 × 10−2 6.25 × 10−2 (continued)

8 Inorganic Semiconductors and Passivation Layers

423

Table 8.110 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.984 2.012 2.039 2.066 2.117 2.164 2.205 2.240 2.269 2.292 2.310 2.324 2.335 2.344 2.353 2.364 2.376

1.175 1.170 1.164 1.157 1.138 1.114 1.086 1.057 1.027 0.998 0.971 0.948 0.928 0.914 0.903 0.897 0.895

710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.825 2.821 2.815 2.807 2.796 2.784 2.771 2.758 2.743 2.729 2.714 2.699 2.685 2.670 2.656 2.643 2.629

0.470 0.431 0.395 0.361 0.330 0.302 0.275 0.251 0.230 0.210 0.192 0.176 0.162 0.149 0.138 0.127 0.118

1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.471 2.466 2.462 2.457 2.453 2.449 2.445 2.442 2.438 2.435 2.432 2.429 2.426 2.423 2.420 2.418

6.17 6.08 6.01 5.93 5.86 5.79 5.73 5.66 5.60 5.55 5.49 5.44 5.39 5.34 5.30 5.26

× × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

8.2.37 MoSe2 (Single Crystal) Data from A. R. Beal and H. P. Hughes [37]. The optical data of a MoSe2 single crystal are shown. Unlike a MoSe2 polycrystalline layer (Fig. 8.36), the light absorption is negligible below E < 1.3 eV in a MoSe2 single crystal (Fig. 8.37, Tables 8.111 and 8.112).

Fig. 8.37 Dielectric function and absorption coefficient of MoSe2 (single crystal) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

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Table 8.111 Tauc-Lorentz parameters of (8.1) and (8.2) for MoSe2 (single crystal) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

109.854 133.264 25.093 140.873 189.347 27.496 119.412 72.551

0.255 0.072 0.171 1.224 0.813 0.625 1.062 3.313

1.444 1.525 1.777 2.175 2.218 2.879 3.875 5.199

1.325 1.441 1.456 1.490 2.041 1.721 3.040 3.432

1.292 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 8.112 Optical constants of MoSe2 (single crystal) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460

2.605 2.685 2.755 2.810 2.847 2.865 2.864 2.851 2.830 2.807 2.787 2.775 2.773 2.783 2.806 2.841 2.889 2.949 3.022 3.108 3.205 3.428 3.669 3.896 4.081 4.217 4.318

2.637 2.615 2.580 2.535 2.485 2.437 2.398 2.373 2.365 2.375 2.402 2.443 2.496 2.557 2.622 2.691 2.760 2.828 2.892 2.950 3.000 3.065 3.067 3.005 2.899 2.780 2.671

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800

4.904 4.936 4.951 4.950 4.936 4.911 4.881 4.850 4.821 4.790 4.759 4.731 4.716 4.726 4.778 4.873 4.968 5.008 4.986 4.932 4.872 4.818 4.777 4.755 4.762 4.823 4.990

1.927 1.812 1.700 1.595 1.500 1.418 1.351 1.298 1.254 1.219 1.197 1.193 1.207 1.237 1.267 1.260 1.184 1.063 0.952 0.878 0.842 0.836 0.856 0.899 0.967 1.060 1.145

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140

5.058 4.995 4.930 4.866 4.806 4.752 4.706 4.669 4.636 4.607 4.580 4.556 4.533 4.513 4.494 4.476 4.459 4.443 4.428 4.414 4.401 4.388 4.376 4.365 4.354 4.343 4.333

0.144 9.16 × 10−2 5.20 × 10−2 2.47 × 10−2 8.41 × 10−3 1.01 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (continued)

8 Inorganic Semiconductors and Passivation Layers

425

Table 8.112 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

470 480 490 500 510 520 530

4.402 4.481 4.562 4.643 4.722 4.795 4.857

2.578 2.495 2.416 2.334 2.244 2.146 2.039

810 820 830 840 850 860 870

5.271 5.424 5.371 5.285 5.219 5.165 5.114

1.078 0.794 0.556 0.428 0.344 0.273 0.206

1150 1160 1170 1180 1190 1200

4.324 4.315 4.306 4.298 4.290 4.282

0 0 0 0 0 0

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

G.E. Jellison Jr., Opt. Mat. 1, 151 (1992) C.M. Herzinger, University of Nebraska-Lincoln (unpublished) (1994) E.D. Palik (ed.), Handbook of Optical Constants of Solids (Academic, New York, 1985) D.E. Aspnes, A.A. Studna, Phys. Rev. B 27, 985 (1983) N.P. Barnes, M.S. Piltch, J. Opt. Soc. Am. 69, 178 (1979) W.C. Dash, R. Newman, Phys. Rev. 99, 1151 (1955) B. Johs, C.M. Herzinger, J.H. Dinan, A. Cornfeld, J.B. Benson, Thin Solid Films 313–314, 137 (1998) C.M. Herzinger, B. Johs, W.A. McGahan, J.A. Woollam, W. Paulson, J. Appl. Phys. 83, 3323 (1998) G. Dingemans, W.M.M. Kessels, J. Vac. Sci. Technol. A 30, 040802 (2012) T. Koida, Y. Kamikawa-Shimizu, A. Yamada, H. Shibata, S. Niki, IEEE J. Photovolt. 5, 956 (2015) G.E. Jellison Jr., F.A. Modine, P. Doshi, A. Rohatgi, Thin Solid Films 313–314, 193 (1998) R.W. Collins, K. Vedam, in Encyclopedia of Applied Physics, vol. 12 (Wiley-VCH, Berlin, 1995), pp. 285–336 S. Kageyama, M. Akagawa, H. Fujiwara, Phys. Rev. B 83, 195205 (2011) M. Sato, S.W. King, W.A. Lanford, P. Henry, T. Fujiseki, H. Fujiwara, J. Non-Cryst. Solids 440, 49–58 (2016) T. Yuguchi, Y. Kanie, N. Matsuki, H. Fujiwara, J. Appl. Phys. 111, 083509 (2012) C.M. Herzinger, H. Yao, P.G. Snyder, F.G. Celii, Y.-C. Kao, B. Johs, J.A. Woollam, J. Appl. Phys. 77, 4677 (1995) D.S. Gerber, G.N. Maracas, IEEE J. Quant. Elect. 29, 2589 (1993) J.B. Theeten, D.E. Aspnes, R.P.H. Chang, J. Appl. Phys. 49, 6097 (1978) A.N. Pikhtin, A.D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978) J.R. Dixon, J.M. Ellis, Phys. Rev. 123, 1560 (1961) D.F. Nelson, E.H. Turner, J. Appl. Phys. 39, 3337 (1968) W.L. Bond, J. Appl. Phys. 36, 1674 (1965) B.O. Seraphin, H.E. Bennet, in Semiconductors and Semimetals, vol. 3 (Academic, New York, 1967), p. 219 C.M. Herzinger, P.G. Snyder, B. Johs, J.A. Woollam, J. Appl. Phys. 77, 1715 (1995) S. Zollner, C. Lin, E. Schoenherr, A. Boehringer, M. Cardona, J. Appl. Phys. 66, 383 (1989) S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information (Kluwer Academic Publishers, Norwell, USA, 1999) J. Lee, R.W. Collins, A.R. Heyd, F. Flack, N. Samarth, Appl. Phys. Lett. 69, 2273 (1996)

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28. D.T.F. Marple, J. Appl. Phys. 35, 539 (1964) 29. J. Li, J. Chen, R.W. Collins, Appl. Phys. Lett. 97, 181909 (2010) 30. S. Minoura, T. Maekawa, K. Kodera, A. Nakane, S. Niki, H. Fujiwara, J. Appl. Phys. 117, 195703 (2015) 31. J. Li, H. Du, J. Yarbrough, A. Norman, K. Jones, G. Teeter, F.L. Terry Jr., D. Levi, Opt. Express 20, A327 (2012) 32. Y. Hirate, H. Tampo, S. Minoura, H. Kadowaki, A. Nakane, K.M. Kim, H. Shibata, S. Niki, H. Fujiwara, J. Appl. Phys. 117, 015702 (2015) 33. A. Nakane, H. Tampo, M. Tamakoshi, S. Fujimoto, K.M. Kim, S. Kim, H. Shibata, S. Niki, H. Fujiwara, J. Appl. Phys. 120, 064505 (2016) 34. S. Kim, K.M. Kim, H. Tampo, H. Shibata, K. Matsubara, S. Niki, Sol. Energy Mater. Sol. Cells 144, 488 (2016) 35. S.G. Choi, J. Kang, J. Li, H. Haneef, N.J. Podraza, C. Beall, S.-H. Wei, S.T. Christensen, I.L. Repins, Appl. Phys. Lett. 106, 043902 (2015) 36. S. Marsillac, N. Barreau, H. Khatri, J. Li, D. Sainju, A. Parikh, N.J. Podraza, R.W. Collins, Phys. Stat. Sol. C 5, 1244 (2008) 37. A.R. Beal, H.P. Hughes, J. Phys. C 12, 881 (1979) 38. M. Richter, C. Schubbert, P. Eraerds, I. Riedel, J. Keller, J. Parisi, T. Dalibor, A. Avellan-Hampe, Thin Solid Films 535, 331 (2013)

Chapter 9

Organic Semiconductors Takemasa Fujiseki, Shohei Fujimoto, Mariano Campoy-Quiles, Maria Isabel Alonso, Takurou N. Murakami, Tetsuhiko Miyadera and Hiroyuki Fujiwara

Abstract The dielectric functions and optical constants of various organic solar-cell materials, a total of 20 semiconductors, are summarized. The organic materials described here include CuPc (fluorinated), MEH-PPV, P3HT, PC60BM, PC70BM, PCDTBT, PEDOT:PSS, PMMA, PTB7, and spiro-OMeTAD. For P3HT and PTB7 semiconductors, the optical properties of those polymers blended with PC60BM and PC70BM are shown. For CuPc (fluorinated), MEH-PPV, P3OT, and PEDOT:PSS layers, the anisotropic optical properties are also indicated. Furthermore, it is established that all the dielectric functions described in this chapter can be parameterized by using several transition peaks calculated from the Tauc-Lorentz model, except for PEDOT:PSS, which is modeled further by incorporating the Drude term.

9.1

Introduction

So far, in an attempt to realize highly efficient solar cells based on organic semiconductors, numerous organic materials have been developed. In general, the organic semiconductors exhibit strong absorption peaks in the visible region and their absorption characteristics are quite important for the interpretation and prediction of the solar cell performance. In organic and organic-inorganic hybrid

T. Fujiseki ⋅ S. Fujimoto ⋅ H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] M. Campoy-Quiles ⋅ M. I. Alonso Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, 08193 Bellaterra, Spain e-mail: [email protected] T. N. Murakami ⋅ T. Miyadera Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba 305-8568, Japan © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_9

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perovskite solar cells, on the other hand, organic layers such as P3HT, PCBM, PEDOT:PSS, PCDTBT and spiro-OMeTAD are applied widely as doped layers. For the ellipsometry characterization of the device structures and the optical simulation, it is necessary to have the optical constants of all the solar-cell component layers. In this chapter, therefore, for the purpose of spectroscopic ellipsometry (SE) characterization and device simulation, the tabulated optical constants of various organic semiconductors at room temperature are provided. In particular, for almost all organic semiconductors, refractive index n and extinction coefficient k are shown in a wavelength (λ) range of 300–1200 nm with steps of 5 nm (300– 400 nm) and 10 nm (400–1200 nm). From these numerical values, the dielectric function (ε = ε1 – iε2) and the absorption coefficient (α) can be calculated quite easily according to ε1 = n2 – k2, ε2 = 2nk and α = 4πk/λ (Sect. 1.2.1). The λ value can also be converted to energy (E) by E = 1239.8/[λ (nm)] eV (1.3). It should be noted that, in the tabulated data, the absolute k value is denoted as “0” when there is no observable light absorption, even though materials may show very small k (or α) values in a certain E region. Often, organic polymer materials consisting of sp2-carbon aromatic chains exhibit strong optical anisotropy. Specifically, when the oscillation direction of the electric field of incident light is parallel to the polymer chains, the light absorption increases significantly due to the optical transition induced by the sp2 π electrons (π → π* transition in Sect. 4.5.2 (Vol. 1)). In spin-coated polymer films, the polymer chains are preferentially aligned parallel to the film surface. Thus, for the electric-field oscillation parallel to the film surface (i.e., ordinary ray), the light absorption is much higher than that when the electric-field oscillation is perpendicular to the film surface (i.e., extraordinary ray). This type of optical anisotropy is classified as uniaxial anisotropy, with the optic (optical) axis perpendicular to the film surface in this case [1]. Consequently, the in-plane optical constants (ordinary ray) are different from the optical constants for the perpendicular direction (extraordinary ray). In this chapter, the complex dielectric constant for the ordinary ray is represented by ε∥ (ε∥ = ε1,∥ − iε2,∥), whereas that for the extraordinary ray is denoted by ε⊥ (ε⊥ = ε1,⊥ − iε2,⊥). For the tabulated data of uniaxial polymer materials (MEH-PPV, P3OT, and PEDOT:PSS), however, only the ε∥ data are shown since the ε∥ component is more important for solar cell devices in which the electric-field oscillation of the incident light is parallel to the device (film) surface. Unfortunately, the tabulated optical data are sometimes insufficient for more complete SE analysis or optical simulation. Accordingly, the dielectric functions of the semiconductors were parameterized assuming the Tauc-Lorentz model described by (1.19)–(1.20). The Tauc-Lorentz model was developed originally to express the dielectric function of amorphous semiconductors [2]. In particular, we found that this model is quite effective for the complete parameterization of almost all organic semiconductors. By combining several Tauc-Lorentz peaks, the dielectric functions of various organic semiconductors are reproduced almost perfectly in a wide photon energy range (E = 1–5 eV) using only one dielectric function model. From the Tauc-Lorentz parameters described in this chapter, (ε1, ε2), (n, k) and α values at arbitrary λ and E can be calculated quite easily. It should be emphasized

9 Organic Semiconductors

429

that the Tauc-Lorentz model is used solely to establish the optical database of various solar-cell component layers. When only limited spectral information is available, however, the Tauc-Lorentz model is also applied to extrapolate the spectrum beyond experimental data to cover the consistent spectral range of 300– 1200 nm. In the actual modeling, the dielectric functions of organic semiconductors were calculated using (8.1) and (8.2), while the dielectric function of PEDOT:PSS was modeled by further incorporating the Drude term (1.27). The calculation example of the Tauc-Lorentz model is shown in (1.26). A free software described in Sect. 2.7 can further be applied to calculate the dielectric function from the Tauc-Lorentz model parameters listed in this chapter. All the parameterizations of the dielectric functions described in this chapter were implemented by the group of Gifu University (T. Fujiseki and S. Fujimoto), unless otherwise noted.

9.2 9.2.1

Optical Data of Organic Semiconductors APFO-3 (F8TBT, PFDTBT) [Poly{2,7(9,9-Dioctylfluorene)-alt-5,5-(4’,7’di-2-Thienyl-2’,1’,3’-Benzothiadiazole)}]

Data from C. Müller, J. Bergqvist, K. Vandewal, K. Tvingstedt, A. S. Anselmo, R. Magnusson, M. I. Alonso, E. Moons, H. Arwin, M. Campoy-Quiles and O. Inganäs [3]. The optical data have been extracted from a sample fabricated by a spin-coating process (Fig. 9.1 and Tables 9.1, 9.2).

Fig. 9.1 a Chemical structure and b dielectric function of APFO-3 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

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Table 9.1 Tauc-Lorentz parameters of (8.1) and (8.2) for APFO-3 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

25.678 11.055 4.061 24.971 6.125 78.248

0.192 0.173 0.182 0.393 0.584 6.832

2.079 2.210 2.326 3.065 4.472 11.350

1.849 1.872 1.872 2.645 3.978 3.579

0.021 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

Table 9.2 Optical constants of APFO-3. The optical data reported by Müller et al. are shown λ (nm)

n

k

λ (nm)

n

k

n

k

300

1.615

0.131

540

1.773

0.742

λ (nm) 880

1.830

0.005

305

1.601

0.135

550

1.910

0.744

890

1.827

0.005

310

1.587

0.140

560

2.035

0.704

900

1.825

0.006

315

1.574

0.147

570

2.136

0.637

910

1.822

0.006

320

1.562

0.156

580

2.216

0.555

920

1.819

0.007

325

1.550

0.166

590

2.277

0.459

930

1.817

0.007

330

1.538

0.178

600

2.314

0.347

940

1.815

0.008

335

1.527

0.193

610

2.311

0.229

950

1.813

0.008

340

1.518

0.209

620

2.271

0.130

960

1.810

0.009

345

1.509

0.229

630

2.211

0.063

970

1.808

0.009

350

1.502

0.251

640

2.152

0.025

980

1.807

0.009

355

1.498

0.276

650

2.101

0.005

990

1.805

0.010

360

1.498

0.304

660

2.060

0

1000

1.803

0.010

365

1.503

0.336

670

2.027

0

1010

1.802

0.010

370

1.515

0.370

680

2.001

0

1020

1.800

0.011

375

1.536

0.404

690

1.978

0

1030

1.798

0.011

380

1.567

0.436

700

1.960

0

1040

1.797

0.011

385

1.609

0.462

710

1.944

0

1050

1.796

0.011

390

1.662

0.476

720

1.930

0

1060

1.794

0.012

395

1.721

0.472

730

1.918

0

1070

1.793

0.012

400

1.777

0.449

740

1.908

0

1080

1.792

0.012

410

1.848

0.356

750

1.899

0

1090

1.791

0.012

420

1.845

0.253

760

1.890

0

1100

1.790

0.013

430

1.796

0.184

770

1.883

0

1110

1.788

0.013

440

1.734

0.153

780

1.876

0

1120

1.787

0.013

450

1.672

0.150

790

1.869

0

1130

1.786

0.013

460

1.615

0.166

800

1.864

0

1140

1.785

0.013

470

1.565

0.200

810

1.858

0

1150

1.784

0.014

480

1.522

0.251

820

1.853

0.001

1160

1.783

0.014

490

1.491

0.320

830

1.849

0.002

1170

1.783

0.014

500

1.478

0.406

840

1.845

0.002

1180

1.782

0.014

510

1.495

0.506

850

1.841

0.003

1190

1.781

0.014

520

1.550

0.608

860

1.837

0.004

1200

1.780

0.014

530

1.646

0.694

870

1.834

0.004

9 Organic Semiconductors

9.2.2

431

APFO-Green9 [Poly{2,7-(9,9-Dioctylfluorene)-alt-5,5(5,10-di-2-Thienyl-2,3,7,8-Tetraphenyl-Pyrazino[2,3-g]Quinoxaline)}]

Data: unpublished results of M. Campoy-Quiles. The characterization results are described in [4] and refractive index data at different temperatures are shown in the supplementary information of [4]. Data for blends of APFO-Green9 and PC70BM can be found in [5] (Fig. 9.2 and Tables 9.3, 9.4).

9.2.3

Fluorinated CuPc (F16CuPc) [Fluorinated Copper Phthalocyanine]

The optical data correspond to those shown in Fig. 15.3a (Chap. 15 in Vol. 1). Partial data can also be found in M. I. Alonso, M. Garriga, J. O. Ossó, F. Schreiber, E. Barrena, and H. Dosch [6]. The optical data have been extracted from a

Fig. 9.2 a Chemical structure and b dielectric function of APFO-Green9 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 9.3 Tauc-Lorentz parameters of (8.1) and (8.2) for APFO-Green9

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

5.582 0.492 6.766 8.439 33.773

0.259 0.312 0.627 0.539 1.698

1.553 1.670 2.823 2.999 3.348

1.155 1.092 2.218 2.200 3.343

2.762 0 0 0 0

= = = = =

1 2 3 4 5

432

T. Fujiseki et al.

Table 9.4 Optical constants of APFO-Green9. The optical data obtained by Campoy-Quiles et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

1.654 1.645 1.637 1.633 1.634 1.641 1.656 1.681 1.714 1.753 1.801 1.898 1.981 2.031 2.049 2.044 2.028 2.006 1.981 1.957 1.933 1.912 1.892 1.874 1.857 1.843 1.829 1.817 1.806 1.796 1.787

0.233 0.243 0.258 0.278 0.302 0.330 0.360 0.390 0.417 0.440 0.454 0.454 0.416 0.351 0.279 0.214 0.162 0.123 0.093 0.073 0.059 0.050 0.045 0.044 0.044 0.047 0.051 0.056 0.062 0.069 0.076

610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910

1.778 1.770 1.763 1.756 1.749 1.744 1.740 1.738 1.737 1.740 1.745 1.759 1.775 1.806 1.839 1.885 1.939 1.988 2.040 2.086 2.117 2.134 2.150 2.150 2.143 2.137 2.125 2.112 2.099 2.087 2.075

0.085 0.095 0.105 0.117 0.131 0.145 0.162 0.181 0.202 0.225 0.251 0.278 0.308 0.336 0.364 0.386 0.400 0.403 0.391 0.365 0.329 0.287 0.242 0.201 0.164 0.132 0.106 0.084 0.066 0.052 0.041

920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.063 2.052 2.042 2.033 2.024 2.016 2.009 2.003 1.996 1.990 1.985 1.981 1.976 1.972 1.969 1.966 1.963 1.960 1.957 1.955 1.953 1.950 1.948 1.946 1.945 1.943 1.942 1.940 1.939

0.032 0.025 0.019 0.014 0.010 0.007 0.005 0.003 0.002 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

perfluorinated CuPc film (see Fig. 9.3a) fabricated by evaporation at 49 °C. Although the optical properties have been obtained from a perfluorinated CuPc sample, conventional hydrogenated CuPc shows similar optical properties. The uniaxial anisotropy of the film was originated both by the molecular anisotropy and by the ordering, resulting in an optic axis in the plane of the film. In this case, the ordinary component, ε∥, represents an optical response related to the plane of the molecules, which is not the plane of the film (Tables 9.5, 9.6 and 9.7).

9 Organic Semiconductors

433

Fig. 9.3 a Chemical structure and b dielectric function of perfluorinated CuPc at room temperature. In (b), ε∥ and ε⊥ show the ordinary and extraordinary dielectric function components of the film, although in this case the subindices ∥ and ⊥ do not refer to the film but are related to contributions nearly parallel or perpendicular to the molecular planes, respectively. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.5 Tauc-Lorentz parameters of (8.1) and (8.2) for ε∥ of perfluorinated CuPc

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

6.882 4.208 1.359 22.538 46.863 44.611 114.552

0.125 0.191 0.262 1.140 0.362 0.380 2.537

1.615 1.747 1.933 3.242 3.259 4.550 5.932

1.376 1.177 0.388 2.338 3.022 4.377 4.629

0.725 0 0 0 0 0 0

Table 9.6 Tauc-Lorentz parameters of (8.1) and (8.2) for ε⊥ of perfluorinated CuPc

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

0.713 0.150 0.043 8.831 0.082 82.689

0.337 0.234 0.146 1.100 0.343 14.454

1.743 1.973 2.102 3.419 3.994 7.275

0.753 1 × 10−4 1 × 10−4 2.432 1.796 4.269

0.890 0 0 0 0 0

= = = = = = =

= = = = = =

1 2 3 4 5 6 7

1 2 3 4 5 6

434

T. Fujiseki et al.

Table 9.7 Optical constants for the ordinary ray (N∥ = n∥ − ik∥) in perfluorinated CuPc calculated by the Tauc-Lorentz model λ (nm)

n∥

k∥

λ (nm)

n∥

k∥

λ (nm)

n∥

k∥

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.421 1.423 1.431 1.443 1.461 1.483 1.510 1.542 1.580 1.622 1.671 1.725 1.786 1.852 1.921 1.984 2.027 2.043 2.035 2.015 1.991 1.945 1.906 1.865 1.821 1.775 1.729 1.682 1.634 1.586 1.538 1.488 1.438 1.386

0.496 0.528 0.559 0.591 0.621 0.650 0.677 0.702 0.724 0.742 0.755 0.762 0.760 0.746 0.713 0.659 0.585 0.505 0.434 0.377 0.334 0.274 0.228 0.188 0.157 0.134 0.119 0.110 0.108 0.111 0.121 0.137 0.160 0.191

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.334 1.282 1.231 1.187 1.160 1.164 1.209 1.303 1.445 1.619 1.794 1.931 2.017 2.063 2.098 2.151 2.231 2.320 2.382 2.405 2.406 2.413 2.443 2.480 2.486 2.457 2.413 2.367 2.326 2.289 2.257 2.229 2.204 2.182

0.233 0.288 0.359 0.452 0.569 0.706 0.854 0.995 1.106 1.163 1.154 1.092 1.015 0.953 0.922 0.910 0.889 0.832 0.743 0.653 0.586 0.543 0.501 0.429 0.333 0.247 0.185 0.143 0.114 0.094 0.079 0.068 0.060 0.053

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.163 2.145 2.129 2.115 2.102 2.090 2.080 2.069 2.060 2.051 2.043 2.035 2.028 2.022 2.015 2.009 2.004 1.998 1.993 1.988 1.984 1.979 1.975 1.971 1.968 1.964 1.961 1.957 1.954 1.951 1.948 1.946 1.943

0.048 0.043 0.040 0.037 0.034 0.031 0.029 0.027 0.026 0.024 0.023 0.022 0.021 0.020 0.019 0.018 0.017 0.016 0.016 0.015 0.015 0.014 0.014 0.013 0.013 0.012 0.012 0.012 0.011 0.011 0.011 0.010 0.010

9 Organic Semiconductors

9.2.4

435

MEH-PPV [Poly{2-Methoxy-5-(2’-Ethyl-Hexyloxy)p-Phenylenevinylene}]

Data from M. Tammer and A. P. Monkman [7]. The optical data have been extracted from a sample fabricated by a spin-coating process (Fig. 9.4 and Tables 9.8, 9.9, 9.10).

Fig. 9.4 a Chemical structure and b dielectric functions of MEH-PPV at room temperature. In (b), ε∥ and ε⊥ show the dielectric functions parallel (ordinary) and perpendicular (extraordinary) to the thin film surface, respectively. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.8 Tauc-Lorentz parameters of (8.1) and (8.2) for ε∥ of MEH-PPV

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

26.539 10.150 5.165 1.735 3.807 74.534

0.188 0.205 0.253 0.289 0.424 9.432

2.281 2.397 2.524 2.693 3.680 4.750

2.025 1.998 1.915 1.950 3.179 4.005

1.591 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

436

T. Fujiseki et al.

Table 9.9 Tauc-Lorentz parameters of (8.1) and (8.2) for ε⊥ of MEH-PPV Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

0.047 7.471 0.894 0.057 43.389

0.960 0.233 0.766 0.246 4.682

1.734 2.372 2.622 3.258 11.406

0.382 2.242 1.448 2.352 3.214

0.527 0 0 0 0

= = = = =

1 2 3 4 5

Table 9.10 Optical constants for the ordinary ray (N∥ = n∥ − ik∥) in MEH-PPV calculated by the Tauc-Lorentz model λ (nm)

n∥

k∥

λ (nm)

n∥

k∥

300

1.470

0.092

540

2.271

0.550

305

1.458

0.098

550

2.328

0.364

310

1.448

0.107

560

2.279

315

1.441

0.118

570

320

1.437

0.130

325

1.438

330

λ (nm)

n∥

k∥

880

1.731

0

890

1.729

0

0.193

900

1.727

0

2.191

0.092

910

1.725

0

580

2.110

0.042

920

1.723

0

0.141

590

2.045

0.017

930

1.721

0

1.443

0.149

600

1.993

0.006

940

1.719

0

335

1.450

0.150

610

1.954

0.002

950

1.718

0

340

1.454

0.144

620

1.923

0.001

960

1.716

0

345

1.450

0.136

630

1.899

0

970

1.715

0

350

1.440

0.129

640

1.879

0

980

1.714

0

355

1.426

0.127

650

1.863

0

990

1.712

0

360

1.412

0.129

660

1.849

0

1000

1.711

0

365

1.398

0.134

670

1.836

0

1010

1.710

0

370

1.384

0.141

680

1.825

0

1020

1.708

0

375

1.370

0.150

690

1.816

0

1030

1.707

0

380

1.356

0.160

700

1.807

0

1040

1.706

0

385

1.343

0.172

710

1.799

0

1050

1.705

0

390

1.330

0.185

720

1.792

0

1060

1.704

0

395

1.316

0.201

730

1.786

0

1070

1.703

0

400

1.303

0.218

740

1.780

0

1080

1.702

0

410

1.276

0.260

750

1.775

0

1090

1.701

0

420

1.250

0.315

760

1.770

0

1100

1.701

0

430

1.231

0.389

770

1.765

0

1110

1.700

0

440

1.232

0.485

780

1.761

0

1120

1.699

0

450

1.270

0.589

790

1.757

0

1130

1.698

0

460

1.342

0.675

800

1.753

0

1140

1.697

0

470

1.419

0.744

810

1.750

0

1150

1.697

0

480

1.522

0.817

820

1.747

0

1160

1.696

0

490

1.663

0.852

830

1.744

0

1170

1.695

0

500

1.793

0.841

840

1.741

0

1180

1.695

0

510

1.922

0.823

850

1.738

0

1190

1.694

0

520

2.061

0.756

860

1.736

0

1200

1.693

0

530

2.163

0.664

870

1.733

0

9 Organic Semiconductors

9.2.5

437

P3HT [Poly(3-Hexylthiophene)]

Data from M. Campoy-Quiles, J. Nelson, D. D. C. Bradley and P. G. Etchegoin [8]. The optical data have been extracted from a P3HT layer formed on a fused silica substrate using a spin-coating process (Fig. 9.5 and Tables 9.11, 9.12).

Fig. 9.5 a Chemical structure and b dielectric function of P3HT at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.11 Tauc-Lorentz parameters of (8.1) and (8.2) for P3HT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

29.026 15.858 7.716 1.957 0.721 58.901

0.158 0.224 0.347 0.412 0.395 6.156

2.039 2.209 2.393 2.659 3.025 3.863

1.824 1.813 1.730 1.748 1.842 3.862

1.875 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

438

T. Fujiseki et al.

Table 9.12 Optical constants of P3HT calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.450 1.436 1.422 1.407 1.393 1.379 1.367 1.354 1.342 1.329 1.317 1.304 1.292 1.279 1.267 1.256 1.246 1.238 1.234 1.235 1.241 1.263 1.275 1.275 1.279 1.304 1.349 1.400 1.449 1.508 1.594 1.703 1.809 1.893

0.101 0.101 0.104 0.108 0.114 0.122 0.131 0.140 0.150 0.162 0.174 0.188 0.203 0.220 0.239 0.261 0.285 0.313 0.342 0.373 0.403 0.449 0.482 0.523 0.584 0.655 0.718 0.768 0.816 0.874 0.931 0.961 0.956 0.940

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.975 2.091 2.224 2.302 2.312 2.328 2.410 2.510 2.514 2.440 2.353 2.276 2.215 2.165 2.126 2.095 2.070 2.049 2.031 2.015 2.000 1.988 1.977 1.966 1.957 1.949 1.941 1.934 1.927 1.921 1.915 1.910 1.905 1.900

0.938 0.930 0.862 0.742 0.647 0.612 0.579 0.453 0.272 0.141 0.068 0.031 0.013 0.004 0.001 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.896 1.891 1.888 1.884 1.880 1.877 1.874 1.871 1.868 1.865 1.863 1.860 1.858 1.856 1.854 1.852 1.850 1.848 1.846 1.844 1.842 1.841 1.839 1.838 1.836 1.835 1.834 1.832 1.831 1.830 1.829 1.828 1.827

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

9.2.6

439

P3HT:PC60BM (Blend Ratio 1:1) [Poly (3-Hexylthiophene):(6,6)-Phenyl-C61-Butyric Acid Methyl Ester]

Data from C. J. M. Emmott, J. A. Röhr, M. Campoy-Quiles, T. Kirchartz, A. Urbina, N. J. Ekins-Daukes, and J. Nelson [9] (Supplementary Information) (Fig. 9.6 and Tables 9.13, 9.14).

Fig. 9.6 a Chemical structure and b dielectric function of P3HT:PC60BM at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 9.13 Tauc-Lorentz parameters of (8.1) and (8.2) for P3HT:PC60BM

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

16.475 24.496 11.627 1.794 77.305

0.199 0.274 0.500 0.687 3.771

2.024 2.189 2.429 3.619 4.448

1.856 2.016 1.866 1.860 3.449

1.494 0 0 0 0

= = = = =

1 2 3 4 5

440

T. Fujiseki et al.

Table 9.14 Optical constants of P3HT:PC60BM. The optical data reported by Emmott et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.757 1.745 1.733 1.720 1.707 1.703 1.700 1.713 1.727 1.733 1.740 1.735 1.730 1.722 1.714 1.704 1.695 1.686 1.677 1.668 1.659 1.640 1.625 1.615 1.613 1.623 1.647 1.688 1.741 1.807 1.876 1.940 1.999 2.042

0.323 0.312 0.301 0.299 0.298 0.309 0.320 0.323 0.327 0.312 0.298 0.285 0.273 0.268 0.264 0.262 0.261 0.262 0.262 0.267 0.271 0.287 0.312 0.343 0.385 0.428 0.475 0.518 0.551 0.568 0.568 0.553 0.520 0.479

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.074 2.102 2.135 2.148 2.135 2.120 2.126 2.141 2.137 2.112 2.075 2.039 2.009 1.985 1.965 1.951 1.940 1.931 1.923 1.915 1.908 1.900 1.894 1.888 1.881 1.876 1.872 1.868 1.864 1.860 1.858 1.855 1.852 1.849

0.437 0.398 0.356 0.291 0.239 0.214 0.196 0.156 0.099 0.054 0.023 0.006 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.845 1.842 1.839 1.836 1.833 1.830 1.827 1.824 1.821 1.817 1.814 1.811 1.808 1.805 1.802 1.799 1.796 1.793 1.789 1.786 1.783 1.780 1.777 1.774 1.771 1.768 1.765 1.761 1.758 1.755 1.752 1.749 1.746

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

9.2.7

441

P3HT:PC70BM (Blend Ratio 1:1) [Poly (3-Hexylthiophene):(6,6)-Phenyl-C71-Butyric Acid Methyl Ester]

Data from C. J. M. Emmott, J. A. Röhr, M. Campoy-Quiles, T. Kirchartz, A. Urbina, N. J. Ekins-Daukes, and J. Nelson [9] (Supplementary Information) (Fig. 9.7 and Tables 9.15, 9.16).

Fig. 9.7 a Chemical structure and b dielectric function of P3HT:PC70BM at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 9.15 Tauc-Lorentz parameters of (8.1) and (8.2) for P3HT:PC70BM

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

30.647 14.683 9.281 0.171 1.300 85.280

0.199 0.190 0.703 3.986 0.920 3.141

2.025 2.199 2.387 2.644 3.247 4.061

1.880 2.016 1.572 1 × 10−4 1.672 3.474

1.772 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

442

T. Fujiseki et al.

Table 9.16 Optical constants of P3HT:PC70BM. The optical data reported by Emmott et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.804 1.795 1.786 1.770 1.753 1.734 1.715 1.697 1.679 1.663 1.648 1.638 1.628 1.623 1.619 1.623 1.626 1.628 1.630 1.630 1.629 1.632 1.635 1.638 1.643 1.656 1.680 1.716 1.760 1.811 1.866 1.921 1.975 2.026

0.313 0.291 0.269 0.254 0.239 0.233 0.227 0.229 0.231 0.240 0.248 0.262 0.275 0.291 0.307 0.320 0.334 0.340 0.346 0.356 0.366 0.386 0.407 0.432 0.462 0.499 0.538 0.573 0.602 0.622 0.632 0.633 0.626 0.614

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.076 2.133 2.200 2.242 2.245 2.257 2.291 2.326 2.327 2.288 2.236 2.191 2.156 2.128 2.108 2.092 2.077 2.062 2.048 2.035 2.024 2.014 2.006 1.998 1.990 1.984 1.978 1.972 1.967 1.962 1.957 1.953 1.949 1.945

0.599 0.580 0.541 0.467 0.411 0.382 0.346 0.278 0.188 0.114 0.071 0.050 0.041 0.036 0.033 0.030 0.024 0.019 0.017 0.015 0.014 0.014 0.013 0.013 0.013 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.941 1.936 1.932 1.928 1.924 1.919 1.915 1.911 1.907 1.903 1.898 1.894 1.890 1.886 1.881 1.877 1.873 1.869 1.865 1.860 1.856 1.852 1.848 1.843 1.839 1.835 1.831 1.827 1.822 1.818 1.814 1.810 1.805

0.012 0.012 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010

9 Organic Semiconductors

9.2.8

443

P3OT [Poly(3-Octylthiophene)]

Data from U. Zhokhavets, G. Gobsch, H. Hoppe and N. S. Sariciftci [10]. The optical data have been extracted from a P3OT layer fabricated by a spin-coating process (Fig. 9.8 and Tables 9.17, 9.18, 9.19).

Fig. 9.8 a Chemical structure and b dielectric functions of P3OT at room temperature. In (b), ε∥ and ε⊥ show the dielectric functions parallel (ordinary) and perpendicular (extraordinary) to the thin film surface, respectively. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated results obtained from the Tauc-Lorentz model Table 9.17 Tauc-Lorentz parameters of (8.1) and (8.2) for ε∥ of P3OT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

1 2 3 4 5 6 7

14.417 8.118 2.993 1.738 1.248 0.503 21.870

0.191 0.221 0.210 0.210 0.255 0.356 0.199

2.024 2.201 2.334 2.445 2.575 2.772 6.018

1.830 1.830 1.830 1.830 1.830 1.828 3.947

1.884 0 0 0 0 0 0

Table 9.18 Tauc-Lorentz parameters of (8.1) and (8.2) for ε⊥ of P3OT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

4.054 0.236 2.077 1.854 0.732 0.100 81.090

0.207 0.141 0.328 0.440 0.339 0.278 3.543

1.990 2.152 2.239 2.442 2.633 2.886 3.852

1.815 1.815 1.815 1.735 2.078 1.813 3.850

1.776 0 0 0 0 0 0

= = = = = = =

= = = = = = =

1 2 3 4 5 6 7

444

T. Fujiseki et al.

Table 9.19 Optical constants for the ordinary ray (N∥ = n∥ − ik∥) in P3OT calculated by the Tauc-Lorentz model λ (nm)

n∥

k∥

λ (nm)

n∥

k∥

λ (nm)

n∥

k∥

310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540

1.549 1.540 1.532 1.524 1.516 1.508 1.500 1.493 1.485 1.478 1.470 1.463 1.455 1.447 1.439 1.431 1.422 1.414 1.405 1.387 1.371 1.359 1.356 1.359 1.364 1.383 1.428 1.477 1.532 1.604 1.667 1.735 1.795

0.041 0.044 0.046 0.049 0.052 0.055 0.058 0.062 0.066 0.070 0.074 0.079 0.084 0.089 0.095 0.102 0.109 0.118 0.127 0.150 0.180 0.218 0.260 0.302 0.349 0.409 0.461 0.496 0.532 0.549 0.550 0.545 0.521

550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.847 1.913 1.965 1.976 1.974 1.988 2.016 2.024 1.999 1.958 1.918 1.884 1.857 1.836 1.820 1.807 1.796 1.786 1.777 1.770 1.763 1.757 1.752 1.747 1.742 1.738 1.734 1.731 1.727 1.724 1.721 1.719 1.716

0.500 0.467 0.400 0.332 0.291 0.263 0.217 0.147 0.081 0.039 0.016 0.005 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.714 1.711 1.709 1.707 1.705 1.703 1.702 1.700 1.699 1.697 1.696 1.694 1.693 1.692 1.691 1.690 1.688 1.687 1.686 1.685 1.685 1.684 1.683 1.682 1.681 1.680 1.680 1.679 1.678 1.678 1.677 1.676 1.676

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

9.2.9

445

PC60BM (Aka PCBM, [60]PCBM, PC61BM) [(6,6)Phenyl-C61-Butyric Acid Methyl Ester]

Data from M. Campoy-Quiles, J. Nelson, D. D. C. Bradley and P. G. Etchegoin [8]. The optical data have been extracted from a PC60BM layer formed on a fused silica substrate using a spin-coating process (Fig. 9.9 and Tables 9.20, 9.21).

Fig. 9.9 a Chemical structure and b dielectric function of PC60BM at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.20 Tauc-Lorentz parameters of (8.1) and (8.2) for PC60BM

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

4.497 16.877 7.436 45.755 11.350

1.366 0.550 0.723 0.787 10.278

3.011 3.593 4.318 4.501 5.140

1.649 2.771 2.593 3.840 1.232

2.249 0 0 0 0

= = = = =

1 2 3 4 5

446

T. Fujiseki et al.

Table 9.21 Optical constants of PC60BM calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.150 2.131 2.109 2.093 2.088 2.099 2.129 2.175 2.230 2.283 2.322 2.341 2.343 2.334 2.320 2.304 2.289 2.276 2.265 2.256 2.249 2.240 2.234 2.230 2.227 2.223 2.219 2.215 2.209 2.203 2.196 2.190 2.183 2.177

0.681 0.642 0.622 0.621 0.633 0.652 0.669 0.676 0.664 0.629 0.578 0.521 0.467 0.422 0.387 0.360 0.339 0.324 0.312 0.301 0.292 0.276 0.261 0.244 0.228 0.212 0.195 0.180 0.165 0.152 0.139 0.128 0.118 0.108

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.170 2.164 2.158 2.152 2.146 2.141 2.135 2.130 2.125 2.121 2.116 2.112 2.107 2.103 2.099 2.096 2.092 2.088 2.085 2.081 2.078 2.075 2.072 2.069 2.067 2.064 2.062 2.059 2.057 2.054 2.052 2.050 2.048 2.046

0.100 0.092 0.085 0.079 0.073 0.067 0.062 0.057 0.053 0.049 0.045 0.042 0.039 0.036 0.033 0.030 0.028 0.026 0.024 0.022 0.020 0.018 0.017 0.015 0.014 0.013 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.005

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.043 2.041 2.040 2.038 2.036 2.034 2.032 2.031 2.029 2.027 2.026 2.024 2.023 2.022 2.020 2.019 2.018 2.017 2.016 2.015 2.014 2.013 2.012 2.012 2.011 2.010 2.009 2.009 2.008 2.007 2.007 2.006 2.005

0.004 0.003 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

447

9.2.10 PC70BM (Aka [70]PCBM, PC71BM) [(6,6)Phenyl-C71-Butyric Acid Methyl Ester] Data from A. Guerrero, B. Dörling, T. Ripolles-Sanchis, M. Aghamohammadi, E. Barrena, M. Campoy-Quiles and G. Garcia-Belmonte [11] (Supplementary Information) (Fig. 9.10 and Tables 9.22, 9.23).

Fig. 9.10 a Chemical structure and b dielectric function of PC70BM at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.22 Tauc-Lorentz parameters of (8.1) and (8.2) for PC70BM

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

4.363 15.347 4.593 3.568 90.660 43.177

0.346 0.679 0.422 0.818 4.935 1.588

1.766 2.160 2.558 3.256 3.948 4.295

1.581 1.740 2.015 1.722 3.945 3.032

1.615 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

448

T. Fujiseki et al.

Table 9.23 Optical constants of PC70BM calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.134 2.134 2.127 2.115 2.099 2.080 2.060 2.041 2.022 2.006 1.994 1.986 1.982 1.984 1.989 1.997 2.006 2.015 2.021 2.026 2.027 2.023 2.014 2.004 1.997 1.997 2.008 2.032 2.063 2.092 2.112 2.125 2.135 2.147

0.578 0.532 0.491 0.456 0.426 0.403 0.385 0.374 0.368 0.367 0.370 0.376 0.383 0.390 0.395 0.397 0.395 0.390 0.382 0.372 0.362 0.346 0.336 0.335 0.343 0.357 0.374 0.386 0.388 0.376 0.358 0.340 0.327 0.315

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.161 2.176 2.191 2.203 2.210 2.213 2.211 2.205 2.196 2.185 2.174 2.164 2.155 2.146 2.139 2.133 2.125 2.117 2.109 2.099 2.090 2.080 2.071 2.063 2.056 2.049 2.044 2.039 2.034 2.030 2.026 2.022 2.019 2.016

0.302 0.286 0.267 0.243 0.217 0.190 0.164 0.140 0.120 0.103 0.089 0.078 0.068 0.060 0.052 0.043 0.035 0.027 0.019 0.013 0.008 0.004 0.002 0.001 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.013 2.010 2.007 2.005 2.003 2.000 1.998 1.996 1.994 1.992 1.991 1.989 1.987 1.986 1.984 1.983 1.981 1.980 1.979 1.978 1.976 1.975 1.974 1.973 1.972 1.971 1.970 1.969 1.968 1.967 1.967 1.966 1.965

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

449

9.2.11 PCDTBT [Poly{N-9-Heptadecanyl2,7-Carbazole-alt-5,5-(4’,7’-di-2-Thienyl-2’,1’,3’Benzothiadiazole)}] Data: unpublished results of M. Campoy-Quiles. The preparation and analysis of a PCDTBT layer are described in [11]. The extinction coefficient data have been shown in [12] (Fig. 9.11 and Tables 9.24, 9.25).

Fig. 9.11 a Chemical structure and b dielectric function of PCDTBT at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.24 Tauc-Lorentz parameters of (8.1) and (8.2) for PCDTBT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

47.521 17.312 7.933 2.754 33.209 9.082 83.250

0.210 0.199 0.225 0.219 0.320 0.403 1.495

2.028 2.144 2.287 2.448 3.022 3.220 4.327

1.829 1.834 1.832 1.833 2.640 2.512 3.941

2.020 0 0 0 0 0 0

= = = = = = =

1 2 3 4 5 6 7

450

T. Fujiseki et al.

Table 9.25 Optical constants of PCDTBT calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.589 1.549 1.509 1.475 1.448 1.425 1.406 1.390 1.377 1.370 1.369 1.376 1.396 1.431 1.484 1.553 1.633 1.714 1.789 1.860 1.931 2.055 2.061 1.965 1.854 1.758 1.681 1.625 1.594 1.606 1.676 1.770 1.837 1.918

0.254 0.253 0.264 0.286 0.313 0.342 0.375 0.412 0.453 0.500 0.551 0.609 0.670 0.732 0.789 0.834 0.859 0.863 0.851 0.830 0.798 0.666 0.480 0.362 0.326 0.341 0.388 0.461 0.559 0.677 0.784 0.835 0.870 0.922

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.036 2.139 2.225 2.345 2.483 2.586 2.664 2.726 2.732 2.674 2.589 2.504 2.431 2.372 2.326 2.292 2.264 2.240 2.220 2.203 2.187 2.173 2.161 2.149 2.139 2.130 2.121 2.113 2.106 2.099 2.092 2.087 2.081 2.076

0.948 0.932 0.925 0.918 0.855 0.751 0.638 0.495 0.328 0.185 0.091 0.039 0.013 0.002 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.071 2.066 2.062 2.058 2.054 2.050 2.047 2.043 2.040 2.037 2.034 2.031 2.029 2.026 2.024 2.021 2.019 2.017 2.015 2.013 2.011 2.009 2.008 2.006 2.004 2.003 2.001 2.000 1.998 1.997 1.996 1.994 1.993

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

451

9.2.12 PCPDTBT [Poly{2,6-(4,4-bis-(2-Ethylhexyl)4H-Cyclopenta[2,1-b;3,4-b’]-Dithiophene)-alt-4,7(2,1,3-Benzothiadiazole)}] Data from A. Guerrero, B. Dörling, T. Ripolles-Sanchis, M. Aghamohammadi, E. Barrena, M. Campoy-Quiles and G. Garcia-Belmonte [11] (Supplementary Information) (Fig. 9.12 and Tables 9.26, 9.27).

Fig. 9.12 a Chemical structure and b dielectric function of PCPDTBT at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.26 Tauc-Lorentz parameters of (8.1) and (8.2) for PCPDTBT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j j

16.531 15.494 5.166 1.233 0.269 8.980 0.334 2.847 0.063 21.461

0.116 0.189 0.239 0.296 0.300 0.216 0.232 0.229 0.212 4.019

1.539 1.615 1.776 1.959 2.189 2.853 3.197 3.017 3.374 4.290

1.396 1.326 1.289 1.084 0.631 2.477 1.325 2.320 1 × 10−4 3.723

2.157 0 0 0 0 0 0 0 0 0

= = = = = = = = = =

1 2 3 4 5 6 7 8 9 10

452

T. Fujiseki et al.

Table 9.27 Optical constants of PCPDTBT calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.441 1.429 1.415 1.401 1.386 1.369 1.351 1.333 1.313 1.292 1.270 1.249 1.240 1.258 1.290 1.305 1.317 1.351 1.397 1.426 1.445 1.531 1.599 1.653 1.703 1.656 1.587 1.528 1.479 1.437 1.400 1.367 1.339 1.318

0.084 0.084 0.085 0.088 0.092 0.098 0.107 0.119 0.133 0.153 0.179 0.217 0.270 0.324 0.353 0.371 0.405 0.442 0.455 0.454 0.464 0.486 0.439 0.407 0.307 0.212 0.176 0.172 0.183 0.203 0.229 0.263 0.304 0.355

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.309 1.316 1.338 1.366 1.387 1.402 1.417 1.444 1.485 1.532 1.579 1.620 1.663 1.715 1.783 1.862 1.936 1.995 2.040 2.086 2.150 2.239 2.342 2.438 2.511 2.567 2.614 2.634 2.608 2.550 2.485 2.423 2.370 2.323

0.414 0.475 0.528 0.566 0.596 0.629 0.671 0.720 0.765 0.799 0.824 0.847 0.875 0.908 0.936 0.945 0.934 0.914 0.900 0.899 0.907 0.905 0.873 0.807 0.721 0.629 0.523 0.396 0.271 0.175 0.112 0.072 0.046 0.030

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.284 2.250 2.222 2.197 2.176 2.156 2.140 2.125 2.111 2.099 2.088 2.078 2.069 2.060 2.052 2.044 2.037 2.031 2.025 2.019 2.014 2.008 2.004 1.999 1.995 1.991 1.987 1.983 1.979 1.976 1.973 1.970 1.967

0.020 0.014 0.010 0.007 0.005 0.004 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

9.2.13 PEDOT:PSS [Poly(3,4-Ethylenedioxythiophene): Poly(4-Styrensulfonate)] Data from L. A. A. Pettersson, S. Ghosh and O. Inganäs [13]. The optical data have been extracted from the multi-sample analysis of PEDOT:PSS layers formed on

9 Organic Semiconductors

453

SiO2-covered crystalline Si and fused silica substrates using a spin-coating process. The thermal annealing of the PEDOT:PSS samples were also perfomred at 120 °C for 2 min to enhance the conductivity. The electrical conductivity of the PEDOT: PSS layer in the direction parallel to the sample surface is 0.94 S/cm (Fig. 9.13 and Tables 9.28, 9.29, 9.30).

Fig. 9.13 a Chemical structure and b dielectric functions of PEDOT:PSS at room temperature. In (b), ε∥ and ε⊥ show the dielectric functions parallel (ordinary) and perpendicular (extraordinary) to the thin film surface, respectively. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model combined with the Drude model [(11.1) and (11.2)] Table 9.28 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ε∥ of PEDOT: PSS Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 Drude

0.446 100.873 0.678 1.302 188.455 1.810

0.532 0.613 1.893 0.285 0.880 0.631

1.520 5.169 5.240 5.439 6.073 –

1.204 5.004 1.815 4.730 5.736 –

1.822 0 0 0 0 –

Table 9.29 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ε⊥ of PEDOT: PSS Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 Drude

2.203 0.845 124.649 336.897 54.486 0.459

0.740 1.654 0.581 0.946 0.507 1.512

2.547 5.226 5.239 5.942 6.124 –

2.652 1.443 5.047 5.941 5.602 –

1.594 0 0 0 0 –

454

T. Fujiseki et al.

Table 9.30 Optical constants for the ordinary ray (N∥ = n∥ − ik∥) in PEDOT:PSS. The optical data reported by Pettersson et al. are shown λ (nm)

n∥

k∥

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.642 1.636 1.631 1.624 1.620 1.616 1.611 1.607 1.602 1.598 1.593 1.590 1.585 1.582 1.579 1.575 1.572 1.568 1.565 1.563 1.559 1.555 1.549 1.543 1.538 1.533 1.527 1.523 1.517 1.512 1.508 1.503 1.498 1.493

2.03 1.90 1.84 1.76 1.76 1.67 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.76 1.76 1.76 1.76 1.76 1.77 1.85 1.94 2.02 2.10 2.19 2.27 2.44 2.61 2.77 2.95 3.11 3.28 3.44

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n∥

k∥

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.488 1.483 1.477 1.473 1.468 1.463 1.458 1.453 1.449 1.445 1.44 1.437 1.432 1.428 1.424 1.420 1.416 1.412 1.408 1.404 1.400 1.396 1.393 1.388 1.383 1.380 1.375 1.371 1.367 1.363 1.358 1.354 1.349 1.343

3.70 × 3.96 × 4.12 × 4.37 × 4.54 × 4.79 × 5.04 × 5.29 × 5.55 × 5.88 × 6.19 × 6.47 × 6.82 × 7.06 × 7.33 × 7.70 × 7.98 × 8.26 × 8.57 × 8.91 × 9.20 × 9.49 × 9.77 × 0.102 0.104 0.107 0.11 0.113 0.115 0.118 0.121 0.124 0.127 0.13

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n∥

k∥

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.339 1.334 1.329 1.323 1.317 1.312 1.307 1.302 1.296 1.289 1.283 1.278 1.272 1.267 1.260 1.254 1.248 1.242 1.236 1.230 1.224 1.219 1.213 1.208 1.202 1.197 1.192 1.186 1.180 1.176 1.170 1.166 1.162

0.133 0.136 0.140 0.143 0.146 0.150 0.154 0.158 0.162 0.167 0.171 0.176 0.181 0.186 0.191 0.197 0.203 0.209 0.215 0.220 0.225 0.229 0.234 0.240 0.249 0.257 0.267 0.276 0.282 0.287 0.296 0.306 0.315

9 Organic Semiconductors

455

9.2.14 PMMA [Poly(Methyl Methacrylate)] Data from M. Campoy-Quiles, J. Nelson, D. D. C. Bradley and P. G. Etchegoin [8]. The optical data have been extracted from a PMMA layer formed on a fused silica substrate using a spin-coating process. While PMMA is not per se a photovoltaic material, this material is often used within the field. The optical data of a thick PMMA substrate are shown in Fig. 13.6 (Chap. 13) (Fig. 9.14 and Tables 9.31, 9.32).

Fig. 9.14 a Chemical structure and b dielectric function of PMMA at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.31 Tauc-Lorentz parameters of (8.1) and (8.2) for PMMA

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1

1.819

0.311

7.043

0.027

1.937

456

T. Fujiseki et al.

Table 9.32 Optical constants of PMMA calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.526 1.523 1.521 1.520 1.518 1.516 1.515 1.514 1.512 1.511 1.510 1.509 1.508 1.507 1.506 1.505 1.504 1.504 1.503 1.502 1.502 1.500 1.499 1.498 1.497 1.496 1.496 1.495 1.494 1.494 1.493 1.493 1.492 1.492

0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.491 1.491 1.490 1.490 1.490 1.489 1.489 1.489 1.489 1.488 1.488 1.488 1.488 1.487 1.487 1.487 1.487 1.487 1.486 1.486 1.486 1.486 1.486 1.486 1.486 1.485 1.485 1.485 1.485 1.485 1.485 1.485 1.485 1.485

0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.485 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.484 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483 1.483

0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

9 Organic Semiconductors

457

9.2.15 PTB7 [Poly{[4,8-bis[(2-Ethylhexyl)Oxy]Benzo [1,2-b:4,5-b’]Dithiophene-2,6-Diyl][3-Fluoro-2[(2-Ethylhexyl)Carbonyl]Thieno[3,4-b] Thiophenediyl]}] Data from M. R. Hammond, R. J. Kline, A. A. Herzing, L. J. Richter, D. S. Germack, H.-W. Ro, C. L. Soles, D. A. Fischer, T. Xu, L. Yu, M. F. Toney and D. M. DeLongchamp [14]. Although PTB7 films formed by a spin-coating process exhibit optical anisotropy, only the dielectric function parallel to the thin film surface (ordinary, ε∥) is shown (Fig. 9.15 and Tables 9.33, 9.34).

Fig. 9.15 a Chemical structure and b dielectric function of PTB7 at room temperature. In (b), only the dielectric function for ordinary ray (ε∥) is shown. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 9.33 Tauc-Lorentz parameters of (8.1) and (8.2) for PTB7

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

31.263 6.497 1.350 14.175 0.425 2.103 146.963

0.191 0.284 0.451 0.926 0.932 1.002 9.858

1.800 1.997 3.068 3.777 5.005 6.233 10.718

1.574 1.532 2.595 3.346 1 × 10−4 3.713 6.224

0.783 0 0 0 0 0 0

= = = = = = =

1 2 3 4 5 6 7

458

T. Fujiseki et al.

Table 9.34 Optical constants of PTB7. The optical data reported by Hammond et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.671 1.676 1.679 1.682 1.683 1.682 1.679 1.676 1.670 1.660 1.647 1.633 1.622 1.612 1.605 1.598 1.592 1.588 1.585 1.584 1.582 1.572 1.563 1.552 1.537 1.523 1.511 1.497 1.479 1.463 1.445 1.430 1.415 1.403

0.174 0.169 0.164 0.157 0.148 0.139 0.130 0.120 0.109 0.098 0.091 0.088 0.089 0.094 0.099 0.104 0.109 0.115 0.120 0.123 0.123 0.127 0.131 0.135 0.142 0.150 0.155 0.162 0.177 0.192 0.215 0.243 0.280 0.323

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.398 1.404 1.420 1.445 1.478 1.523 1.585 1.665 1.748 1.819 1.875 1.933 2.011 2.121 2.242 2.353 2.405 2.395 2.343 2.279 2.219 2.169 2.128 2.095 2.068 2.047 2.027 2.011 1.996 1.986 1.975 1.964 1.954 1.947

0.373 0.427 0.482 0.536 0.589 0.645 0.695 0.729 0.739 0.730 0.723 0.729 0.741 0.729 0.680 0.566 0.418 0.276 0.169 0.100 0.058 0.035 0.022 0.015 0.012 0.011 0.010 0.009 0.009 0.008 0.009 0.009 0.009 0.009

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.942 1.934 1.932 1.925 1.921 1.919 1.917 1.911 1.909 1.905 1.902 1.897 1.894 1.889 1.881 1.873 1.867 1.862 1.854 1.848 1.843 1.838 1.836 1.832 1.829 1.827 1.825 1.823 1.822 1.820 1.820 1.819 1.818

0.010 0.010 0.012 0.010 0.010 0.010 0.011 0.011 0.010 0.009 0.009 0.009 0.008 0.008 0.009 0.012 0.012 0.015 0.020 0.023 0.025 0.025 0.025 0.027 0.026 0.025 0.024 0.023 0.022 0.020 0.019 0.017 0.016

9 Organic Semiconductors

459

9.2.16 PTB7:PC70BM (Blend Ratio 1:1.5) [Poly{[4,8-bis [(2-Ethylhexyl)Oxy]Benzo [1,2-b:4,5-b’] Dithiophene-2,6-Diyl][3-Fluoro-2-[(2-Ethylhexyl) Carbonyl]Thieno[3,4-b]Thiophenediyl]}:(6,6)Phenyl-C71-Butyric Acid Methyl Ester] Data from C. J. M. Emmott, J. A. Röhr, M. Campoy-Quiles, T. Kirchartz, A. Urbina, N. J. Ekins-Daukes, and J. Nelson [9] (Supplementary Information) (Fig. 9.16 and Tables 9.35, 9.36).

Fig. 9.16 a Chemical structure and b dielectric function of PTB7:PC70BM at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 9.35 Tauc-Lorentz parameters of (8.1) and (8.2) for PTB7:PC70BM

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

15.800 3.565 7.477 3.653 1.609 73.603 0.290

0.237 0.230 0.526 0.507 0.705 4.011 0.592

1.796 1.991 2.120 2.558 3.231 4.209 4.212

1.564 1.657 1.694 2.009 1.624 3.129 1.555

1.695 0 0 0 0 0 0

= = = = = = =

1 2 3 4 5 6 7

460

T. Fujiseki et al.

Table 9.36 Optical constants of PTB7:PC70BM. The optical data reported by Emmott et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.920 1.920 1.920 1.912 1.905 1.893 1.882 1.870 1.858 1.845 1.833 1.823 1.814 1.811 1.808 1.814 1.820 1.822 1.824 1.823 1.822 1.818 1.811 1.801 1.789 1.784 1.787 1.798 1.810 1.820 1.824 1.826 1.826 1.827

0.412 0.384 0.356 0.334 0.312 0.297 0.282 0.272 0.263 0.259 0.255 0.258 0.260 0.268 0.275 0.280 0.284 0.278 0.273 0.270 0.267 0.261 0.256 0.254 0.260 0.274 0.290 0.301 0.306 0.305 0.303 0.305 0.310 0.321

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.832 1.842 1.857 1.876 1.894 1.913 1.938 1.968 2.000 2.025 2.041 2.056 2.077 2.114 2.157 2.200 2.221 2.216 2.191 2.161 2.131 2.105 2.082 2.063 2.047 2.033 2.022 2.012 2.002 1.995 1.988 1.981 1.975 1.971

0.333 0.348 0.360 0.368 0.375 0.382 0.389 0.390 0.382 0.366 0.350 0.342 0.341 0.334 0.315 0.269 0.206 0.143 0.094 0.060 0.039 0.027 0.020 0.015 0.012 0.011 0.009 0.008 0.008 0.008 0.008 0.008 0.008 0.008

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.966 1.962 1.959 1.955 1.952 1.949 1.946 1.943 1.941 1.939 1.937 1.935 1.932 1.929 1.924 1.920 1.915 1.910 1.905 1.901 1.896 1.891 1.886 1.882 1.877 1.872 1.868 1.863 1.858 1.853 1.849 1.844 1.839

0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008

9 Organic Semiconductors

461

9.2.17 Si-PCPDTBT [Poly{[4, 40-bis(2-Ethylhexyl) Dithieno (3,2-b:20,30-d)Silole]-2,6-Diyl-alt-[4,7-bis (2-Thienyl)-2,1,3-Benzothiadiazole]-5,50-Diyl}] Data: unpublished results of M. Campoy-Quiles. The preparation and analysis of a Si-PCPDTBT layer are described in [15]. Data for the Si-PCPDTBT:PC70BM are shown in the supplementary information of [15]. Extinction coefficient data have been shown in [12] (Fig. 9.17 and Tables 9.37, 9.38).

Fig. 9.17 a Chemical structure and b dielectric function of Si-PCPDTBT at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.37 Tauc-Lorentz parameters of (8.1) and (8.2) for Si-PCPDTBT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

32.524 12.197 3.292 1.033 18.709 11.818 70.597

0.146 0.265 0.299 0.292 0.435 0.577 8.627

1.606 1.765 1.945 2.167 2.846 3.870 4.603

1.422 1.395 1.390 1.398 2.498 3.408 3.785

1.696 0 0 0 0 0 0

= = = = = = =

1 2 3 4 5 6 7

462

T. Fujiseki et al.

Table 9.38 Optical constants of Si-PCPDTBT calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.555 1.561 1.571 1.581 1.588 1.587 1.578 1.563 1.546 1.529 1.514 1.500 1.489 1.480 1.473 1.468 1.466 1.465 1.468 1.473 1.483 1.515 1.565 1.618 1.644 1.630 1.591 1.545 1.501 1.463 1.433 1.408 1.388 1.375

0.231 0.236 0.238 0.233 0.220 0.204 0.190 0.180 0.177 0.179 0.185 0.194 0.206 0.219 0.234 0.249 0.265 0.283 0.301 0.319 0.338 0.370 0.383 0.362 0.311 0.258 0.227 0.219 0.230 0.253 0.284 0.321 0.365 0.415

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.371 1.382 1.409 1.444 1.477 1.503 1.529 1.563 1.610 1.667 1.725 1.780 1.833 1.892 1.961 2.038 2.110 2.167 2.206 2.240 2.288 2.371 2.491 2.612 2.678 2.672 2.618 2.547 2.478 2.415 2.361 2.315 2.275 2.243

0.472 0.532 0.588 0.631 0.661 0.691 0.728 0.771 0.811 0.842 0.861 0.873 0.886 0.900 0.909 0.902 0.876 0.839 0.806 0.790 0.791 0.792 0.758 0.656 0.498 0.338 0.214 0.129 0.075 0.042 0.021 0.010 0.003 0.001

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.216 2.193 2.174 2.156 2.141 2.128 2.115 2.104 2.094 2.085 2.076 2.068 2.060 2.053 2.047 2.041 2.035 2.030 2.025 2.020 2.015 2.011 2.007 2.003 1.999 1.996 1.992 1.989 1.986 1.983 1.980 1.977 1.975

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

463

9.2.18 Spiro-OMeTAD [2,2’,7,7’-Tetrakis-(N, N-di-pMethoxyphenylamine) 9,9’-Spirobifluorene] Data from M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T. N. Murakami, S. Fujimoto, M. Chikamatsu and H. Fujiwara [16]. The optical data have been extracted from a spiro-OMeTAD layer formed on a ZnO-coated crystalline Si substrate using a spin-coating process. The thermal annealing of the sample was performed at 100 °C. The spiro-OMeTAD layer doped with Li (LiTFSI) has been characterized (Fig. 9.18 and Tables 9.39, 9.40).

Fig. 9.18 a Chemical structure and b dielectric function of spiro-OMeTAD at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 9.39 Tauc-Lorentz parameters of (8.1) and (8.2) for spiro-OMeTAD reported by Shirayama et al.

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

55.872 4.914 3.033 4.482

0.283 0.303 0.555 0.001

3.102 3.358 4.035 5.183

2.855 2.826 2.850 2.850

2.256 0 0 0

= = = =

1 2 3 4

464

T. Fujiseki et al.

Table 9.40 Optical constants of spiro-OMeTAD calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.592 1.617 1.640 1.653 1.654 1.647 1.637 1.625 1.616 1.609 1.609 1.619 1.643 1.682 1.729 1.770 1.809 1.859 1.929 2.010 2.073 2.068 1.980 1.907 1.862 1.834 1.814 1.799 1.786 1.776 1.767 1.760 1.753 1.747

0.269 0.280 0.276 0.262 0.249 0.241 0.240 0.247 0.261 0.282 0.310 0.344 0.379 0.407 0.419 0.421 0.425 0.432 0.426 0.386 0.305 0.120 0.027 0.002 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.742 1.738 1.734 1.730 1.727 1.723 1.721 1.718 1.716 1.713 1.711 1.710 1.708 1.706 1.705 1.703 1.702 1.700 1.699 1.698 1.697 1.696 1.695 1.694 1.693 1.692 1.692 1.691 1.690 1.689 1.689 1.688 1.688 1.687

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.686 1.686 1.685 1.685 1.684 1.684 1.684 1.683 1.683 1.682 1.682 1.682 1.681 1.681 1.681 1.680 1.680 1.680 1.679 1.679 1.679 1.679 1.678 1.678 1.678 1.678 1.677 1.677 1.677 1.677 1.677 1.676 1.676

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

465

9.2.19 TQ1 [Poly{2,3-bis-(3-Octyloxyphenyl) Quinoxaline-5,8-Diyl-alt-Thiophene-2,5-Diyl}] Data for TQ1 and its blends with PC70BM are described in M. Campoy-Quiles, C. Müller, M. Garriga, E. Wang, O. Inganäs, M. I. Alonso [5]. The preparation and analysis of a TQ1 layer can be found in [17] (Fig. 9.19 and Tables 9.41, 9.42).

Fig. 9.19 a Chemical structure and b dielectric function of TQ1 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.41 Tauc-Lorentz parameters of (8.1) and (8.2) for TQ1

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

7.453 1.494 0.384 14.465 66.752

0.287 0.227 0.260 0.714 10.063

1.938 2.045 2.215 3.233 13.570

1.448 1.516 1.514 2.674 2.549

0.003 0 0 0 0

= = = = =

1 2 3 4 5

466

T. Fujiseki et al.

Table 9.42 Optical constants of TQ1 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.650 1.646 1.642 1.639 1.637 1.636 1.637 1.639 1.644 1.652 1.662 1.676 1.692 1.711 1.730 1.749 1.765 1.777 1.784 1.785 1.782 1.763 1.737 1.708 1.681 1.656 1.633 1.613 1.594 1.576 1.559 1.543 1.527 1.514

0.171 0.175 0.180 0.187 0.194 0.202 0.211 0.220 0.230 0.239 0.247 0.254 0.258 0.258 0.253 0.243 0.227 0.208 0.186 0.164 0.142 0.107 0.084 0.071 0.067 0.069 0.074 0.084 0.095 0.109 0.125 0.145 0.170 0.202

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.507 1.508 1.517 1.532 1.556 1.599 1.667 1.751 1.840 1.926 2.001 2.053 2.078 2.079 2.065 2.043 2.019 1.996 1.974 1.953 1.935 1.918 1.904 1.890 1.878 1.868 1.858 1.849 1.841 1.834 1.828 1.822 1.816 1.812

0.239 0.282 0.325 0.369 0.421 0.476 0.522 0.544 0.540 0.512 0.459 0.387 0.309 0.238 0.179 0.134 0.100 0.075 0.056 0.041 0.031 0.023 0.017 0.012 0.008 0.006 0.004 0.002 0.001 0.001 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.807 1.804 1.800 1.796 1.793 1.790 1.788 1.785 1.783 1.780 1.778 1.776 1.774 1.772 1.771 1.769 1.767 1.766 1.764 1.763 1.762 1.760 1.759 1.758 1.757 1.756 1.755 1.754 1.753 1.752 1.751 1.750 1.749

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 Organic Semiconductors

467

9.2.20 DPPTTT [Thieno(3,2-b)ThiopheneDiketopyrrolopyrrole] Data from M. S. Vezie, S. Few, I. Meager, G. Pieridou, B. Dörling, R. S. Ashraf, A. R. Goñi, H. Bronstein, I. McCulloch, S. C. Hayes, M. Campoy-Quiles and J. Nelson [12] (Fig. 9.20 and Tables 9.43, 9.44).

Fig. 9.20 a Chemical structure and b dielectric function of DPPTTT at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 9.43 Tauc-Lorentz parameters of (8.1) and (8.2) for DPPTTT

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

26.722 2.368 4.202 7.090 15.258

0.168 0.288 0.443 0.727 4.552

1.536 1.731 1.921 2.822 9.949

1.329 0.866 1.304 2.095 1.563

1.325 0 0 0 0

= = = = =

1 2 3 4 5

468

T. Fujiseki et al.

Table 9.44 Optical constants of DPPTTT calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.460 1.454 1.447 1.440 1.434 1.427 1.421 1.415 1.410 1.404 1.400 1.396 1.392 1.390 1.388 1.388 1.389 1.391 1.396 1.402 1.411 1.435 1.464 1.495 1.519 1.532 1.531 1.520 1.500 1.476 1.450 1.423 1.398 1.375

0.147 0.150 0.155 0.160 0.165 0.171 0.178 0.185 0.193 0.201 0.211 0.221 0.232 0.243 0.256 0.269 0.282 0.296 0.310 0.323 0.336 0.357 0.369 0.367 0.353 0.331 0.308 0.289 0.277 0.274 0.278 0.290 0.309 0.334

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.354 1.337 1.326 1.321 1.324 1.335 1.357 1.386 1.423 1.464 1.505 1.547 1.589 1.634 1.687 1.751 1.825 1.903 1.974 2.033 2.078 2.116 2.158 2.214 2.294 2.396 2.503 2.585 2.621 2.612 2.574 2.522 2.467 2.415

0.366 0.403 0.446 0.494 0.545 0.598 0.650 0.699 0.742 0.779 0.810 0.838 0.866 0.896 0.926 0.952 0.966 0.964 0.946 0.918 0.892 0.874 0.868 0.869 0.865 0.836 0.764 0.650 0.514 0.386 0.281 0.203 0.147 0.107

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.367 2.325 2.288 2.255 2.227 2.202 2.181 2.162 2.146 2.131 2.118 2.105 2.094 2.084 2.074 2.065 2.057 2.049 2.041 2.034 2.028 2.022 2.016 2.010 2.005 2.000 1.995 1.991 1.986 1.982 1.978 1.974 1.971

0.079 0.060 0.047 0.037 0.031 0.027 0.025 0.022 0.020 0.019 0.017 0.015 0.014 0.013 0.012 0.011 0.010 0.009 0.008 0.008 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.003 0.003 0.003 0.002 0.002

9 Organic Semiconductors

469

References 1. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, West Sussex, UK, 2007) 2. G.E. Jellison Jr., F.A. Modine, Appl. Phys. Lett. 69, 371 (1996); Erratum, Appl. Phys. Lett. 69, 2137 (1996) 3. C. Müller, J. Bergqvist, K. Vandewal, K. Tvingstedt, A.S. Anselmo, R. Magnusson, M.I. Alonso, E. Moons, H. Arwin, M. Campoy-Quiles, O. Inganäs, J. Mater. Chem. 21, 10676 (2011) 4. C. Müller, L.M. Andersson, O. Peña-Rodríguez, M. Garriga, O. Inganäs, M. Campoy-Quiles, Macromolecules 46, 7325 (2013) 5. M. Campoy-Quiles, C. Müller, M. Garriga, E. Wang, O. Inganäs, M.I. Alonso, Thin Solid Films 571, 371 (2014) 6. M.I. Alonso, M. Garriga, J.O. Ossó, F. Schreiber, E. Barrena, H. Dosch, J. Chem. Phys. 119, 6335 (2003) 7. M. Tammer, A.P. Monkman, Adv. Mater. 14, 210 (2002) 8. M. Campoy-Quiles, J. Nelson, D.D.C. Bradley, P.G. Etchegoin, Phys. Rev. B 76, 235206 (2007) 9. C.J.M. Emmott, J.A. Röhr, M. Campoy-Quiles, T. Kirchartz, A. Urbina, N.J. Ekins-Daukes, J. Nelson, Energy Environ. Sci. 8, 1317 (2015) 10. U. Zhokhavets, G. Gobsch, H. Hoppe, N.S. Sariciftci, Thin Solid Films 451–452, 69 (2004) 11. A. Guerrero, B. Dörling, T. Ripolles-Sanchis, M. Aghamohammadi, E. Barrena, M. Campoy-Quiles, G. Garcia-Belmonte, ACS Nano 7, 4637 (2013) 12. M.S. Vezie, S. Few, I. Meager, G. Pieridou, B. Dörling, R.S. Ashraf, A.R. Goñi, H. Bronstein, I. McCulloch, S.C. Hayes, M. Campoy-Quiles, J. Nelson, Nat. Mater. 15, 746 (2016) 13. L.A.A. Pettersson, S. Ghosh, O. Inganäs, Org. Electron. 3, 143 (2002) 14. M.R. Hammond, R.J. Kline, A.A. Herzing, L.J. Richter, D.S. Germack, H.-W. Ro, C.L. Soles, D.A. Fischer, T. Xu, L. Yu, M.F. Toney, D.M. DeLongchamp, ACS Nano 5, 8248 (2011) 15. T. Kirchartz, T. Agostinelli, M. Campoy-Quiles, W. Gong, J. Nelson, J. Phys. Chem. Lett. 3, 3470 (2012) 16. M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T.N. Murakami, S. Fujimoto, M. Chikamatsu, H. Fujiwara, Phys. Rev. Appl. 5, 014012 (2016) 17. L. Hou, E. Wang, J. Bergqvist, B.V. Andersson, Z. Wang, C. Müller, M. Campoy-Qulies, M.R. Andersson, F. Zhang, O. Inganäs, Adv. Funct. Mater. 21, 3169 (2011)

Chapter 10

Organic-Inorganic Hybrid Perovskites Shohei Fujimoto, Takemasa Fujiseki, Masato Tamakoshi, Akihiro Nakane, Tetsuhiko Miyadera, Takeshi Sugita, Takurou N. Murakami, Masayuki Chikamatsu and Hiroyuki Fujiwara

Abstract The dielectric functions and optical constants of various organic-inorganic hybrid perovskite semiconductors, including HC(NH2)2PbI3, CH3NH3PbI3, CH3NH3PbBr3 and CH3NH3PbCl3, are summarized. For CH3NH3Pb (I, Br)3 alloys, the variation of the dielectric function with Br content, calculated by applying the energy shift model, is presented. This chapter also provides the optical constants of perovskite secondary phases, such as semitransparent δ-phase HC (NH2)2PbI3, PbI2 and CH3NH3I. It has been established that the dielectric functions of all the hybrid perovskite compounds can be parameterized by assuming several transition peaks calculated from the Tauc-Lorentz model. In particular, by incorporating Tauc-Lorentz peaks with very small amplitudes, the absorption coefficient spectra of the hybrid perovskites are reproduced almost perfectly in a quite wide range of α = 102–106 cm−1. In this chapter, the Tauc-Lorentz parameters obtained from the above parameterization scheme are summarized, together with the tabulated optical constants.

10.1

Introduction

The methylammonium lead iodide (MAPbI3; CH3NH3PbI3) and formamidinium lead iodide [FAPbI3; HC(NH2)2PbI3] are direct transition semiconductors with band gaps of 1.61 eV and 1.55 eV, respectively [1], and hybrid perovskite solar cells

S. Fujimoto ⋅ T. Fujiseki ⋅ M. Tamakoshi ⋅ A. Nakane ⋅ H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] T. Miyadera ⋅ T. Sugita ⋅ T. N. Murakami ⋅ M. Chikamatsu Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba 305-8568, Japan © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_10

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with these absorbers exhibit a short-circuit current density (Jsc) of ∼20 mA/cm2 (Chap. 16 in Vol. 1). The optimal device design basically relies on the optical constants of component layers and, particularly in tandem solar cells with hybrid perovskites, accurate optical data are necessary in optimizing complex device structures [2]. Furthermore, the reliable absorber optical constants are of paramount importance in interpreting carrier recombination dynamics in hybrid perovskite solar cells [3]. In this chapter, for the purpose of spectroscopic ellipsometry (SE) characterization and device simulation, the tabulated optical constants of various hybrid perovskite materials at room temperature are provided. The dielectric functions of FAPbI3 and MAPbI3 have been extracted from thin layers fabricated by a laser evaporation technique, in which PbI2 and HC(NH2)2I [or CH3NH3I] source materials are heated by a near-infrared laser [2]. In particular, this technique allows the formation of the smoother perovskite layers, which is critical for accurate determination of optical constants [1] (Chap. 6 in Vol. 1). Unfortunately, solution-processed hybrid perovskites often exhibit quite roughness surfaces with a dimension comparable to the wavelength (λ) of SE light probe and, therefore, extra care is necessary for the SE analysis of these samples (Chap. 6 in Vol. 1). Moreover, since FAPbI3 and MAPbI3 show rather significant phase change in humid air (Chap. 16 in Vol. 1), the SE measurements of laser-evaporated FAPbI3 and MAPbI3 layers were carried out in a N2-filled glove bag without exposing the samples to air, although the MAPbI3 spectra in a high energy region (E ≥ 4.75 eV) were obtained from the measurements in air [2]. The optical properties of δ-phase FAPbI3, PbI2 and CH3NH3I secondary phases, fabricated by laser evaporation, are also determined without air exposure. On the other hand, for MAPb(I1−xBrx)3, the full optical data sets are provided for different Br contents in a complete range of x = 0–1.0. For all the materials described here, refractive index n and extinction coefficient k are shown in a λ range of 300–1200 nm with steps of 5 nm (300–400 nm) and 10 nm (400–1200 nm). From these numerical values, the dielectric function (ε = ε1 – iε2) and the absorption coefficient (α) can be calculated quite easily according to ε1 = n2 − k2, ε2 = 2nk and α = 4πk/λ (Sect. 1.2.1). The λ value can also be converted to energy (E) by E = 1239.8/[λ (nm)] eV (1.3). Unfortunately, the tabulated optical data are sometimes insufficient for more complete SE analysis or optical simulation. Accordingly, all the dielectric functions are parameterized assuming the Tauc-Lorentz model described by (1.19)–(1.20). Although the Tauc-Lorentz model was developed originally to express the dielectric function of amorphous semiconductors [4], this model is quite effective for the complete parameterization of the dielectric functions. In particular, by combining several Tauc-Lorentz peaks, the dielectric functions described in this chapter can be reproduced almost perfectly in a wide photon energy range (E = 1–5 eV) using only one dielectric function model. From the Tauc-Lorentz parameters described in

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this chapter, (ε1, ε2), (n, k) and α values at arbitrary λ and E can be calculated quite easily. It should be emphasized that the Tauc-Lorentz model is used solely to establish the optical database of various solar-cell component layers. When only limited spectral information is available, however, the Tauc-Lorentz model is also applied to extrapolate the spectrum beyond experimental data to cover the consistent spectral range of 300–1200 nm. In the actual modeling, the dielectric functions were calculated using (8.1) and (8.2). The calculation example of the Tauc-Lorentz model is also shown in (1.26). A free software described in Sect. 2.7 can further be applied to calculate the dielectric function from the Tauc-Lorentz model parameters listed in this chapter. All the parameterizations of the dielectric functions described in this chapter were implemented by the group of Gifu University, unless otherwise noted.

10.2

Optical Data of Hybrid Perovskites

10.2.1 FAPbI3 [HC(NH2)2PbI3] Data from M. Kato, T. Fujiseki, T. Miyadera, T. Sugita, S. Fujimoto, M. Tamakoshi, M. Chikamatsu, and H. Fujiwara [5] (see also Fig. 16.5 in Vol. 1). The optical data have been determined by multi-sample SE analysis of cubic FAPbI3 (α phase), formed on SiO2-covered crystalline Si substrates by laser evaporation at room temperature (Fig. 10.1 and Tables 10.1, 10.2).

Fig. 10.1 Dielectric function and absorption coefficient of FAPbI3 (α phase) at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

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Table 10.1 Tauc-Lorentz parameters of (8.1) and (8.2) for FAPbI3 (α phase). The model parameters reported by Kato et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

10.018 8.849 9.041 1.028 20.435 66.516 98.353 131.316

0.099 0.498 0.794 0.171 0.755 0.417 0.657 3.018

1.557 1.566 2.344 2.486 2.712 3.083 3.190 3.897

1.543 1.521 1.618 1.740 2.093 2.726 2.918 3.882

1.462 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 10.2 Optical constants of FAPbI3 (α phase) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.646 1.645 1.649 1.658 1.677 1.704 1.738 1.778 1.824 1.876 1.934 1.997 2.066 2.139 2.215 2.293 2.372 2.449 2.522 2.584 2.627 2.633 2.560 2.490 2.453 2.441

0.855 0.882 0.914 0.951 0.992 1.032 1.069 1.104 1.136 1.164 1.188 1.206 1.218 1.221 1.214 1.197 1.168 1.126 1.068 0.993 0.903 0.717 0.596 0.554 0.543 0.538

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

2.518 2.504 2.490 2.475 2.458 2.442 2.426 2.411 2.396 2.383 2.370 2.359 2.349 2.339 2.331 2.324 2.317 2.311 2.306 2.301 2.296 2.292 2.288 2.284 2.279 2.271

0.279 0.248 0.221 0.196 0.175 0.156 0.141 0.128 0.117 0.107 9.91 × 9.22 × 8.62 × 8.09 × 7.60 × 7.14 × 6.68 × 6.21 × 5.73 × 5.23 × 4.71 × 4.16 × 3.57 × 2.89 × 2.02 × 9.61 ×

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

2.201 0 2.197 0 2.193 0 2.189 0 2.186 0 2.182 0 2.179 0 2.176 0 2.173 0 2.170 0 2.168 0 2.165 0 2.163 0 2.160 0 2.158 0 2.156 0 2.154 0 2.152 0 2.150 0 2.148 0 2.147 0 2.145 0 2.143 0 2.142 0 2.140 0 2.139 0 (continued)

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3

k

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Table 10.2 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

460 470 480 490 500 510 520 530

2.443 2.447 2.451 2.472 2.525 2.552 2.544 2.531

0.527 0.512 0.502 0.503 0.479 0.411 0.354 0.313

800 810 820 830 840 850 860 870

2.258 2.246 2.237 2.229 2.223 2.217 2.211 2.206

1.79 × 10−3 0 0 0 0 0 0 0

1140 1150 1160 1170 1180 1190 1200

2.137 2.136 2.135 2.133 2.132 2.131 2.130

0 0 0 0 0 0 0

10.2.2 MAPbI3 (CH3NH3PbI3) Data from M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T. N. Murakami, S. Fujimoto, M. Chikamatsu, and H. Fujiwara [2] (see also Fig. 16.5 in Vol. 1). The optical data have been determined by multi-sample SE analysis of quite smooth MAPbI3 layers, formed on ZnO-coated crystalline Si substrates by laser evaporation at room temperature.

Fig. 10.2 Dielectric function and absorption coefficient of MAPbI3 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)] Table 10.3 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPbI3. The model parameters reproted by Shirayama et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

1.621 47.677 2.909 39.202

0.024 0.137 0.349 2.391

1.593 1.607 2.553 3.046

1.565 1.593 1.684 1.563

0 1.486 0 0 (continued)

= = = =

1 2 3 4

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Table 10.3 (continued) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

4.955 1.369 1.622 4.137 11.256

0.329 0.354 0.745 0.666 2.053

3.278 3.581 4.726 5.648 7.408

1.764 2.246 2.823 3.839 2.276

0 0 0 0 0

= = = = =

5 6 7 8 9

Table 10.4 Optical constants of MAPbI3 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.580 1.596 1.614 1.636 1.660 1.689 1.725 1.771 1.828 1.892 1.951 2.007 2.072 2.164 2.293 2.447 2.587 2.677 2.714 2.718 2.707 2.678 2.658 2.647 2.644 2.647 2.660 2.688 2.731 2.773 2.793 2.792 2.777 2.758

1.075 1.107 1.141 1.177 1.215 1.256 1.299 1.344 1.384 1.413 1.434 1.460 1.499 1.542 1.568 1.545 1.461 1.339 1.217 1.117 1.041 0.941 0.878 0.834 0.800 0.774 0.755 0.737 0.705 0.648 0.575 0.505 0.447 0.399

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.738 2.718 2.699 2.680 2.663 2.646 2.630 2.615 2.601 2.588 2.576 2.564 2.554 2.546 2.538 2.533 2.529 2.527 2.528 2.531 2.536 2.538 2.531 2.508 2.483 2.461 2.446 2.433 2.422 2.412 2.404 2.396 2.389 2.382

0.360 0.327 0.299 0.274 0.252 0.233 0.216 0.201 0.188 0.177 0.167 0.158 0.150 0.144 0.138 0.132 0.127 0.122 0.115 0.105 8.99 × 6.73 × 3.80 × 1.27 × 3.42 × 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.376 2.370 2.365 2.360 2.355 2.350 2.346 2.342 2.338 2.334 2.331 2.328 2.324 2.321 2.318 2.316 2.313 2.310 2.308 2.305 2.303 2.301 2.299 2.297 2.295 2.293 2.291 2.289 2.287 2.286 2.284 2.283 2.281

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−3

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477

10.2.3 MAPbBr3 (CH3NH3PbBr3) Data from A. M. A. Leguy, P. Azarhoosh, M. I. Alonso, M. Campoy-Quiles, O. J. Weber, J. Yao, D. Bryant, M. T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, and P. R. F. Barnes [6] (see also Fig. 16.5 in Vol. 1). The optical data have been extracted from a MAPbBr3 single crystal (Fig. 10.3, Tables 10.5 and 10.6).

Fig. 10.3 Dielectric function and absorption coefficient of MAPbBr3 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 10.5 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPbBr3 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

14.194 50.951 140.251 48.060 14.262 78.865 6.204 41.650

0.022 0.110 0.090 2.641 1.002 0.663 0.620 0.070

2.258 2.298 2.343 2.425 3.416 3.949 4.466 8.469

2.245 2.257 2.305 2.382 2.412 3.489 2.428 2.905

0.011 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

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Table 10.6 Optical constants of MAPbBr3 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.427 2.478 2.521 2.546 2.548 2.531 2.505 2.479 2.459 2.447 2.442 2.445 2.452 2.460 2.466 2.471 2.472 2.471 2.467 2.461 2.453 2.435 2.415 2.395 2.376 2.358 2.341 2.327 2.316 2.310 2.314 2.340 2.421 2.516

1.009 0.955 0.886 0.808 0.731 0.666 0.619 0.589 0.571 0.560 0.551 0.542 0.528 0.510 0.489 0.465 0.440 0.415 0.391 0.369 0.348 0.312 0.283 0.260 0.242 0.229 0.220 0.216 0.217 0.224 0.239 0.262 0.273 0.142

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.439 2.370 2.323 2.293 2.271 2.253 2.237 2.224 2.212 2.202 2.192 2.184 2.176 2.168 2.162 2.156 2.150 2.145 2.139 2.135 2.130 2.126 2.122 2.118 2.115 2.112 2.108 2.105 2.103 2.100 2.097 2.095 2.092 2.090

3.24 × 10−2 2.06 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.088 2.086 2.084 2.082 2.080 2.078 2.076 2.075 2.073 2.072 2.070 2.069 2.067 2.066 2.065 2.064 2.062 2.061 2.060 2.059 2.058 2.057 2.056 2.055 2.054 2.053 2.052 2.051 2.051 2.050 2.049 2.048 2.048

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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10.2.4 MAPb(I1-xBrx)3 [CH3NH3Pb(I1-xBrx)3] Data: unpublished results of Gifu University. The dielectric functions of MAPb (I1-xBrx)3 alloys with different Br content x are summarized. These dielectric functions have been obtained by applying the energy shift model [7], in which the dielectric function of an alloy is “synthesized” from two known dielectric functions (see also Sect. 10.4.1 in Vol. 1). For this calculation, the dielectric functions of MAPbI3 and MAPbBr3, reported by M. Shirayama et al. [2] and J.-S. Park et al. [8], respectively, were adopted as the end point compositions. In the actual calculation, the band gap bowing effect in the MAPb(I1-xBrx)3 alloy system has also been taken into account. The dielectric functions obtained from this procedure have been parameterized further using the Tauc-Lorentz model and the modeled results are described here. The Tauc-Lorentz parameters and optical constants of x = 0.0 (MAPbI3) are shown in Tables 10.3 and 10.4 (Fig. 10.4, Tables 10.7, 10.8, 10.9, 10.10, 10.11, 10.12, 10.13 and 10.14).

Fig. 10.4 Dielectric functions, optical constants and absorption coefficients of various MAPb (I1-xBrx)3 alloys calculated by the Tauc-Lorentz model [(8.1) and (8.2)]. The MAPb(I1-xBrx)3 dielectric functions in a range of x = 0.25–0.75 represent those calculated from the energy shift model, where the dielectric function of x = 0.0 corresponds to that shown in Fig. 10.2

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Table 10.7 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPb(I1-xBrx)3 (x = 0.25) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

11.185 44.013 30.150 24.972 88.842 30.875 88.986 124.162

0.089 0.113 0.659 0.846 0.823 0.379 0.425 6.451

1.700 1.750 1.792 2.707 2.973 3.368 3.584 4.089

1.677 1.704 1.791 1.887 2.763 2.733 3.444 4.072

1.287 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 10.8 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPb(I1-xBrx)3 (x = 0.50) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

14.467 52.571 24.250 24.333 60.788 26.191 57.244 142.483

0.083 0.100 0.838 0.889 0.822 0.377 0.620 4.840

1.843 1.903 1.993 2.864 3.198 3.509 3.791 4.366

1.827 1.847 1.881 2.032 2.895 2.869 3.405 4.365

1.283 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 10.9 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPb(I1-xBrx)3 (x = 0.75) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

24.343 32.193 62.145 24.011 34.346 5.746 39.177 161.085

0.112 0.606 0.088 1.093 0.647 0.307 0.752 4.956

2.045 2.092 2.098 3.083 3.636 3.709 4.046 4.730

2.019 2.099 2.036 2.139 3.005 2.985 3.345 4.556

1.191 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

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Table 10.10 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPb(I1-xBrx)3 (x = 1.00). The model parameters reported by Park et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

70.13 30.02 8.69 2.76 5.03 11.13 4.70 18.53

0.09 0.60 0.83 0.47 0.58 0.90 1.41 0.77

2.33 2.34 3.10 3.42 3.92 4.36 5.88 9.65

2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25

1.0 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 10.11 Optical constants of MAPb(I1-xBrx)3 (x = 0.25) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.587 1.616 1.652 1.694 1.742 1.796 1.856 1.917 1.974 2.027 2.087 2.173 2.294 2.430 2.539 2.601 2.620 2.614 2.599 2.585 2.573 2.558 2.551 2.552 2.566 2.593

1.095 1.137 1.177 1.216 1.251 1.282 1.306 1.322 1.333 1.347 1.374 1.406 1.416 1.375 1.283 1.170 1.065 0.983 0.922 0.878 0.844 0.794 0.757 0.732 0.712 0.690

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

2.591 2.572 2.554 2.539 2.525 2.513 2.502 2.492 2.483 2.474 2.466 2.458 2.452 2.450 2.456 2.474 2.501 2.507 2.477 2.441 2.412 2.393 2.378 2.365 2.354 2.344

0.279 0.257 0.239 0.224 0.211 0.199 0.188 0.178 0.168 0.160 0.152 0.147 0.145 0.145 0.146 0.142 0.117 6.41 × 10−2 2.08 × 10−2 4.09 × 10−3 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

2.286 0 2.281 0 2.277 0 2.273 0 2.269 0 2.265 0 2.262 0 2.259 0 2.255 0 2.252 0 2.249 0 2.247 0 2.244 0 2.242 0 2.239 0 2.237 0 2.235 0 2.232 0 2.230 0 2.228 0 2.226 0 2.225 0 2.223 0 2.221 0 2.219 0 2.218 0 (continued)

k

482

S. Fujimoto et al.

Table 10.11 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

460 470 480 490 500 510 520 530

2.630 2.658 2.673 2.675 2.667 2.651 2.632 2.611

0.652 0.598 0.538 0.479 0.424 0.377 0.338 0.305

800 810 820 830 840 850 860 870

2.335 2.327 2.320 2.313 2.307 2.301 2.296 2.290

0 0 0 0 0 0 0 0

1140 1150 1160 1170 1180 1190 1200

2.216 2.215 2.213 2.212 2.210 2.209 2.208

0 0 0 0 0 0 0

Table 10.12 Optical constants of MAPb(I1-xBrx)3 (x = 0.50) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.667 1.726 1.791 1.859 1.925 1.982 2.031 2.082 2.152 2.248 2.360 2.455 2.506 2.517 2.509 2.494 2.481 2.469 2.461 2.456 2.453 2.459 2.478 2.507 2.537 2.556

1.157 1.192 1.217 1.230 1.232 1.228 1.227 1.236 1.252 1.255 1.219 1.138 1.035 0.943 0.872 0.821 0.784 0.755 0.733 0.715 0.701 0.679 0.657 0.626 0.581 0.525

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

2.439 2.427 2.416 2.406 2.397 2.387 2.379 2.373 2.373 2.387 2.428 2.478 2.456 2.403 2.363 2.338 2.319 2.304 2.291 2.280 2.270 2.260 2.252 2.245 2.238 2.232

0.223 0.210 0.199 0.188 0.179 0.172 0.168 0.169 0.174 0.183 0.182 0.125 3.98 × 10−2 5.83 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

2.190 0 2.187 0 2.183 0 2.180 0 2.177 0 2.174 0 2.172 0 2.169 0 2.167 0 2.164 0 2.162 0 2.160 0 2.158 0 2.156 0 2.154 0 2.152 0 2.150 0 2.149 0 2.147 0 2.145 0 2.144 0 2.142 0 2.141 0 2.139 0 2.138 0 2.137 0 (continued)

k

10

Organic-Inorganic Hybrid Perovskites

483

Table 10.12 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

460 470 480 490 500 510 520 530

2.561 2.555 2.541 2.523 2.504 2.485 2.468 2.453

0.467 0.414 0.368 0.330 0.299 0.274 0.254 0.237

800 810 820 830 840 850 860 870

2.226 2.220 2.215 2.210 2.206 2.202 2.197 2.194

0 0 0 0 0 0 0 0

1140 1150 1160 1170 1180 1190 1200

2.136 2.134 2.133 2.132 2.131 2.130 2.129

0 0 0 0 0 0 0

Table 10.13 Optical constants of MAPb(I1-xBrx)3 (x = 0.75) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.888 1.961 2.020 2.068 2.116 2.177 2.257 2.341 2.394 2.413 2.410 2.397 2.382 2.368 2.358 2.355 2.358 2.365 2.375 2.387 2.399 2.420 2.434 2.438 2.432 2.420

1.168 1.152 1.129 1.110 1.100 1.095 1.075 1.020 0.936 0.853 0.785 0.734 0.697 0.672 0.656 0.644 0.633 0.623 0.610 0.594 0.576 0.533 0.483 0.433 0.385 0.344

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

2.303 2.295 2.289 2.294 2.337 2.437 2.413 2.338 2.294 2.266 2.246 2.229 2.215 2.203 2.192 2.183 2.174 2.166 2.159 2.152 2.146 2.141 2.136 2.131 2.126 2.122

0.187 0.184 0.188 0.204 0.228 0.173 4.16 × 10−2 1.97 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

2.092 0 2.090 0 2.087 0 2.085 0 2.083 0 2.081 0 2.079 0 2.077 0 2.075 0 2.073 0 2.071 0 2.070 0 2.068 0 2.067 0 2.065 0 2.064 0 2.062 0 2.061 0 2.060 0 2.058 0 2.057 0 2.056 0 2.055 0 2.054 0 2.053 0 2.052 0 (continued)

k

484

S. Fujimoto et al.

Table 10.13 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

460 470 480 490 500 510 520 530

2.405 2.388 2.372 2.357 2.344 2.332 2.322 2.312

0.310 0.282 0.259 0.241 0.226 0.214 0.203 0.194

800 810 820 830 840 850 860 870

2.118 2.114 2.110 2.107 2.104 2.101 2.098 2.095

0 0 0 0 0 0 0 0

1140 1150 1160 1170 1180 1190 1200

2.051 2.050 2.049 2.048 2.047 2.046 2.046

0 0 0 0 0 0 0

Table 10.14 Optical constants of MAPb(I1-xBrx)3 (x = 1.00) calculated by the Tauc-Lorentz model λ (nm) 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420

n 2.122 2.163 2.209 2.255 2.290 2.306 2.303 2.287 2.269 2.254 2.249 2.253 2.267 2.282 2.295 2.302 2.305 2.306 2.306 2.306 2.305 2.303 2.294

k 0.974 0.939 0.903 0.856 0.796 0.730 0.672 0.627 0.599 0.584 0.577 0.573 0.563 0.546 0.523 0.498 0.474 0.452 0.432 0.413 0.394 0.357 0.322

λ (nm) 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760

n 2.379 2.276 2.226 2.195 2.172 2.153 2.138 2.125 2.114 2.104 2.095 2.086 2.079 2.072 2.066 2.060 2.055 2.050 2.045 2.041 2.037 2.033 2.029

k −2

4.67 × 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100

1.998 0 1.996 0 1.995 0 1.993 0 1.991 0 1.990 0 1.988 0 1.987 0 1.985 0 1.984 0 1.983 0 1.981 0 1.980 0 1.979 0 1.978 0 1.977 0 1.976 0 1.975 0 1.974 0 1.973 0 1.972 0 1.971 0 1.970 0 (continued)

10

Organic-Inorganic Hybrid Perovskites

485

Table 10.14 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

430 440 450 460 470 480 490 500 510 520 530

2.282 2.268 2.254 2.242 2.233 2.226 2.219 2.213 2.211 2.238 2.380

0.292 0.268 0.250 0.236 0.226 0.217 0.211 0.210 0.222 0.260 0.244

770 780 790 800 810 820 830 840 850 860 870

2.026 2.023 2.020 2.017 2.014 2.011 2.009 2.007 2.004 2.002 2.000

0 0 0 0 0 0 0 0 0 0 0

1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.969 1.968 1.968 1.967 1.966 1.965 1.965 1.964 1.963 1.963

0 0 0 0 0 0 0 0 0 0

10.2.5 MAPbCl3 (CH3NH3PbCl3) Data from A. M. A. Leguy, P. Azarhoosh, M. I. Alonso, M. Campoy-Quiles, O. J. Weber, J. Yao, D. Bryant, M. T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, and P. R. F. Barnes [6] (see also Fig. 16.5 in Vol. 1). The optical data have been extracted from a MAPbCl3 single crystal (Fig. 10.5, Tables 10.15 and 10.16).

Fig. 10.5 Dielectric function and absorption coefficient of MAPbCl3 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

486

S. Fujimoto et al.

Table 10.15 Tauc-Lorentz parameters of (8.1) and (8.2) for MAPbCl3 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j

24.330 177.556 219.273 34.078 10.013 17.475 209.001

0.012 0.046 0.052 1.516 0.397 1.421 0.053

3.065 3.096 3.125 3.199 4.695 5.279 9.718

3.045 3.043 3.071 3.099 3.733 3.051 6.544

0.076 0 0 0 0 0 0

= = = = = = =

1 2 3 4 5 6 7

Table 10.16 Optical constants of MAPbCl3 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430

2.189 2.173 2.159 2.148 2.138 2.129 2.122 2.115 2.108 2.101 2.094 2.086 2.077 2.067 2.056 2.043 2.028 2.013 2.015 2.209 2.496 2.243 2.156 2.112

0.248 0.239 0.232 0.226 0.220 0.215 0.209 0.204 0.199 0.195 0.191 0.187 0.186 0.186 0.190 0.200 0.221 0.263 0.358 0.532 0.292 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770

1.965 1.959 1.954 1.949 1.944 1.940 1.936 1.932 1.929 1.926 1.923 1.920 1.917 1.915 1.912 1.910 1.908 1.906 1.904 1.902 1.900 1.899 1.897 1.896

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110

1.882 0 1.882 0 1.881 0 1.880 0 1.879 0 1.878 0 1.877 0 1.877 0 1.876 0 1.875 0 1.875 0 1.874 0 1.873 0 1.873 0 1.872 0 1.871 0 1.871 0 1.870 0 1.870 0 1.869 0 1.869 0 1.868 0 1.868 0 1.867 0 (continued)

k

10

Organic-Inorganic Hybrid Perovskites

487

Table 10.16 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

440 450 460 470 480 490 500 510 520 530

2.082 2.060 2.042 2.028 2.015 2.004 1.994 1.986 1.978 1.971

0 0 0 0 0 0 0 0 0 0

780 790 800 810 820 830 840 850 860 870

1.894 1.893 1.891 1.890 1.889 1.888 1.887 1.885 1.884 1.883

0 0 0 0 0 0 0 0 0 0

1120 1130 1140 1150 1160 1170 1180 1190 1200

1.867 1.867 1.866 1.866 1.865 1.865 1.865 1.864 1.864

0 0 0 0 0 0 0 0 0

10.2.6 FAPbI3 (δ Phase) Data from M. Kato, T. Fujiseki, T. Miyadera, T. Sugita, S. Fujimoto, M. Tamakoshi, M. Chikamatsu, and H. Fujiwara [5] (see also Fig. 16.6 in Vol. 1). The optical data have been determined by multi-sample SE analysis of FAPbI3 crystals (δ phase), formed on a PCDTBT(5 nm)/ZnO(50 nm)/crystalline Si substrate structure by laser evaporation at room temperature (Fig. 10.6, Tables 10.17 and 10.18).

Fig. 10.6 Dielectric function of FAPbI3 (δ phase) at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

488

S. Fujimoto et al.

Table 10.17 Tauc-Lorentz parameters of (8.1) and (8.2) for FAPbI3 (δ phase). The model parameters reproted by Kato et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

1.573 15.657 2.182 1.563 0.411 367.887 72.513 3.777 776.547

0.404 1.898 0.232 0.118 0.078 0.233 0.366 0.291 0.202

1.893 2.291 3.127 3.232 3.285 3.439 3.611 4.021 4.638

1.667 2.288 1.690 1.803 1.695 3.411 3.398 3.305 4.388

2.455 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 10.18 Optical constants of FAPbI3 (δ phase) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

2.408 2.408 2.429 2.441 2.447 2.466 2.502 2.553 2.606 2.639 2.640 2.595 2.464 2.286 2.143 2.117 2.414 2.685 2.778 2.800 2.836 2.815 2.734 2.663 2.609 2.567

0.550 0.593 0.609 0.608 0.613 0.624 0.629 0.616 0.572 0.498 0.406 0.299 0.216 0.253 0.393 0.704 0.872 0.814 0.634 0.543 0.455 0.267 0.163 0.113 8.52 × 10−2 6.77 × 10−2

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790

2.378 2.366 2.356 2.347 2.340 2.334 2.328 2.324 2.320 2.317 2.314 2.311 2.307 2.303 2.299 2.295 2.290 2.285 2.281 2.277 2.273 2.270 2.267 2.264 2.262 2.259

1.50 1.53 1.57 1.63 1.69 1.75 1.80 1.82 1.80 1.71 1.56 1.35 1.09 8.26 5.83 3.82 2.29 1.22 0 0 0 0 0 0 0 0

× × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130

2.242 0 2.240 0 2.239 0 2.237 0 2.236 0 2.235 0 2.233 0 2.232 0 2.231 0 2.230 0 2.229 0 2.228 0 2.227 0 2.226 0 2.225 0 2.224 0 2.223 0 2.223 0 2.222 0 2.221 0 2.220 0 2.220 0 2.219 0 2.218 0 2.217 0 2.217 0 (continued)

k

10

Organic-Inorganic Hybrid Perovskites

489

Table 10.18 (continued) λ (nm)

n

k

460 470 480 490 500 510 520 530

2.533 2.505 2.481 2.460 2.440 2.423 2.406 2.391

5.52 4.54 3.73 3.07 2.52 2.08 1.76 1.56

× × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

λ (nm)

n

k

800 810 820 830 840 850 860 870

2.257 2.254 2.252 2.250 2.248 2.247 2.245 2.243

0 0 0 0 0 0 0 0

1140 1150 1160 1170 1180 1190 1200

2.216 2.216 2.215 2.214 2.214 2.213 2.213

0 0 0 0 0 0 0

10.2.7 PbI2 Data from M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T. N. Murakami, S. Fujimoto, M. Chikamatsu, and H. Fujiwara [2] (see also Fig. 16.6 in Vol. 1). The optical data have been determined by multi-sample SE analysis of PbI2 layers, formed on crystalline Si substrates by laser evaporation at room temperature (Fig. 10.7, Tables 10.19 and 10.20).

Fig. 10.7 Dielectric function of PbI2 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

490

S. Fujimoto et al.

Table 10.19 Tauc-Lorentz parameters of (8.1) and (8.2) for PbI2. The model parameters reproted by Shirayama et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

1.087 162.630 38.741 55.440 61.819 75.977 24.014 3.436

0.794 0.124 0.415 0.453 0.200 1.428 0.441 1.381

1.820 2.462 2.644 2.902 3.208 3.829 4.364 5.313

1.720 2.374 2.335 2.316 3.023 2.211 3.376 1.800

1.812 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 10.20 Optical constants of PbI2 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460

2.747 2.813 2.887 2.965 3.040 3.108 3.164 3.209 3.241 3.260 3.270 3.272 3.269 3.265 3.267 3.283 3.321 3.367 3.380 3.363 3.356 3.427 3.575 3.712 3.771 3.764 3.730

2.158 2.121 2.082 2.034 1.976 1.909 1.835 1.759 1.684 1.612 1.548 1.492 1.449 1.418 1.401 1.393 1.381 1.340 1.278 1.245 1.247 1.274 1.237 1.101 0.919 0.757 0.630

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800

3.312 3.255 3.207 3.167 3.133 3.104 3.077 3.054 3.032 3.013 2.995 2.979 2.964 2.950 2.936 2.924 2.912 2.902 2.891 2.882 2.873 2.865 2.857 2.849 2.842 2.836 2.829

7.54 5.99 5.36 5.19 4.96 4.68 4.35 3.96 3.53 3.06 2.56 2.07 1.58 1.14 0 0 0 0 0 0 0 0 0 0 0 0 0

× × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140

2.788 0 2.784 0 2.780 0 2.777 0 2.773 0 2.769 0 2.766 0 2.763 0 2.760 0 2.757 0 2.754 0 2.751 0 2.748 0 2.746 0 2.743 0 2.741 0 2.738 0 2.736 0 2.734 0 2.732 0 2.730 0 2.728 0 2.726 0 2.724 0 2.722 0 2.721 0 2.719 0 (continued)

k

10

Organic-Inorganic Hybrid Perovskites

491

Table 10.20 (continued) λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

470 480 490 500 510 520 530

3.686 3.637 3.621 3.712 3.677 3.499 3.387

0.530 0.462 0.437 0.363 0.115 1.97 × 10−2 1.03 × 10−2

810 820 830 840 850 860 870

2.823 2.818 2.812 2.807 2.802 2.797 2.793

0 0 0 0 0 0 0

1150 1160 1170 1180 1190 1200

2.717 2.716 2.714 2.713 2.711 2.710

0 0 0 0 0 0

10.2.8 CH3NH3I Data from M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T. N. Murakami, S. Fujimoto, M. Chikamatsu, and H. Fujiwara [2] (see also Fig. 16.6 in Vol. 1). The optical data have been extracted from a CH3NH3I layer, formed on ZnO-coated crystalline Si substrates by laser evaporation at room temperature (Fig. 10.8, Tables 10.21 and 10.22).

Fig. 10.8 Dielectric function of CH3NH3I at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

492

S. Fujimoto et al.

Table 10.21 Tauc-Lorentz parameters of (8.1) and (8.2) for CH3NH3I. The model parameters reproted by Shirayama et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

2.018 1.994 0.967 0.608

1.556 0.547 0.444 0.671

3.743 4.601 5.302 6.083

2.200 2.200 2.200 2.200

1.405 0 0 0

= = = =

1 2 3 4

Table 10.22 Optical constants of CH3NH3I calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.463 1.452 1.443 1.436 1.431 1.428 1.425 1.423 1.422 1.420 1.419 1.417 1.415 1.413 1.410 1.407 1.404 1.401 1.398 1.395 1.392 1.386 1.380 1.375 1.369 1.365 1.360 1.356 1.352 1.349 1.345 1.342 1.340 1.337

0.150 0.137 0.128 0.120 0.114 0.108 0.103 9.68 × 9.08 × 8.48 × 7.87 × 7.27 × 6.68 × 6.11 × 5.57 × 5.06 × 4.58 × 4.14 × 3.73 × 3.36 × 3.02 × 2.43 × 1.94 × 1.54 × 1.22 × 9.53 × 7.36 × 5.60 × 4.18 × 3.04 × 2.14 × 1.44 × 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.335 1.333 1.331 1.329 1.327 1.326 1.325 1.323 1.322 1.321 1.320 1.319 1.319 1.318 1.317 1.316 1.316 1.315 1.315 1.314 1.313 1.313 1.312 1.312 1.312 1.311 1.311 1.310 1.310 1.310 1.309 1.309 1.309 1.308

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.308 1.308 1.308 1.307 1.307 1.307 1.307 1.307 1.306 1.306 1.306 1.306 1.306 1.305 1.305 1.305 1.305 1.305 1.305 1.304 1.304 1.304 1.304 1.304 1.304 1.304 1.304 1.303 1.303 1.303 1.303 1.303 1.303

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3

10

Organic-Inorganic Hybrid Perovskites

493

References 1. H. Fujiwara, M. Kato, M. Tamakoshi, T. Miyadera, M. Chikamatsu, Phys. Status Solidi A 215, 1700730 (2018) 2. M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T.N. Murakami, S. Fujimoto, M. Chikamatsu, H. Fujiwara, Phys. Rev. Appl. 5, 014012 (2016) 3. A. Nakane, H. Tampo, M. Tamakoshi, S. Fujimoto, K.M. Kim, S. Kim, H. Shibata, S. Niki, H. Fujiwara, J. Appl. Phys. 120, 064505 (2016) 4. G. E. Jellison, Jr., F. A. Modine, Appl. Phys. Lett. 69, 371 (1996). Erratum, Appl. Phys. Lett. 69, 2137 (1996) 5. M. Kato, T. Fujiseki, T. Miyadera, T. Sugita, S. Fujimoto, M. Tamakoshi, M. Chikamatsu, H. Fujiwara, J. Appl. Phys. 121, 115501 (2017) 6. A.M.A. Leguy, P. Azarhoosh, M.I. Alonso, M. Campoy-Quiles, O.J. Weber, J. Yao, D. Bryant, M.T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, P.R.F. Barnes, Nanoscale 8, 6317 (2016) 7. P.G. Snyder, J.A. Woollam, S.A. Alterovitz, B. Johs, J. Appl. Phys. 68, 5925 (1990) 8. J.-S. Park, S. Choi, Y. Yan, Y. Yang, J.M. Luther, S.-H. Wei, P. Parilla, K. Zhu, J. Phys. Chem. Lett. 6, 4304 (2015)

Chapter 11

Transparent Conductive Oxides Akihiro Nakane, Shohei Fujimoto, Masato Tamakoshi, Takashi Koida, James N. Hilfiker, Gerald E. Jellison Jr., Takurou N. Murakami, Tetsuhiko Miyadera and Hiroyuki Fujiwara

Abstract The dielectric functions and optical constants of various transparent conductive oxide (TCO) materials, which have been incorporated into solar cell devices, are summarized. The TCO materials described here include In2O3:Sn (ITO), In2O3:H, InZnO, SnO2:F, TiO2, and ZnO:Al (or Ga). Oxide layers such as MoOx, NiO, and WO3 are often employed to improve electronic properties at semiconductor interfaces and the optical data of these TCO layers are also described. In conventional solar cells, the free carrier absorption that occurs within the TCO layers reduces the photocurrent largely, and the characterization of the parasitic absorption within the solar cell is quite important. Accordingly, for ITO and doped ZnO layers, the variation of the dielectric function with carrier concentration is presented. Since non-doped TCO layers are widely employed as high-resistive buffer layers, the dielectric functions of non-doped In2O3, SnO2 and ZnO are also described. It is established in this chapter that all the TCO dielectric functions in the whole near-infrared/visible/ultraviolet region (1–5 eV) can be parameterized by the combined use of the Tauc-Lorentz and Drude models. For the modeling with the Tauc-Lorentz model, several transition peaks are assumed in the ultraviolet region to describe the interband transition above the band gap. In this chapter, the parameterization results for all the TCO materials are summarized, together with the tabulated optical constants.

A. Nakane ⋅ S. Fujimoto ⋅ M. Tamakoshi ⋅ H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] T. Koida ⋅ T. N. Murakami ⋅ T. Miyadera Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Japan J. N. Hilfiker J.A. Woollam Co., Inc., 645 M Street, Suite 102, Lincoln, NE 68508, USA G. E. Jellison Jr. Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_11

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Introduction

Transparent conductive oxide (TCO) layers are commonly used as front electrodes in almost all thin-film photovoltaic devices. Unfortunately, these TCO layers exhibit rather strong light absorption due to free carrier absorption, induced by free electrons present within the TCO (Chap. 18 in Vol. 1). In particular, the parasitic light absorption in the TCO reduces the short-circuit current density by ∼3 mA/cm2 (Table 2.1) and thus the suppression of the TCO free carrier absorption is crucial for maximizing the conversion efficiencies (Chap. 2). For the estimation and interpretation of optical losses caused by TCO layers, however, the optical constants of TCO layers need to be characterized. In this chapter, for the purpose of spectroscopic ellipsometry (SE) characterization and device simulation, the tabulated optical constants of various TCO materials at room temperature are provided. In addition, graphene (C), which can be employed as an alternative TCO layer, is also treated here. For all the materials, refractive index n and extinction coefficient k are shown in a wavelength (λ) range of 300–1200 nm with steps of 5 nm (300–400 nm) and 10 nm (400–1200 nm). From these numerical values, the dielectric function (ε = ε1 − iε2) and the absorption coefficient (α) can be calculated quite easily according to ε1 = n2 − k2, ε2 = 2nk and α = 4πk/λ (Sect. 1.2.1). The λ value can also be converted to energy (E) by E = 1239.8/[λ (nm)] eV (1.3). It should be noted that, in the tabulated data, the absolute k value is denoted as “0” when there is no observable light absorption, even though materials may have very small k (or α) values in a certain E region. Unfortunately, the tabulated data are sometimes insufficient for more complete SE analysis or optical simulation. Accordingly, all the TCO dielectric functions were parameterized using the Tauc-Lorentz model described by (1.19)–(1.20). When the TCO exhibited free carrier absorption, the dielectric function was parameterized by further combining the Drude model [see (1.27)]. The Tauc-Lorentz model was developed originally to express the dielectric function of amorphous materials [1], but we found that this model is quite effective for the complete parameterization of light absorption that occurs above the band gap (Eg) of TCO materials. It should be emphasized that the Tauc-Lorentz model is used solely to establish the optical database of numerous solar-cell component layers. In this chapter, the dielectric function of TCO materials is modeled by combining several Tauc-Lorentz peaks with the Drude model: m

ε2 ðEÞ = ∑

Aj Cj E0, j ðE − Eg, j Þ2

j = 1 ½ðE 2

− E0,2 j Þ2

+ Cj2 E 2 E

+

AD Γ . + Γ2 E

E3

ð11:1Þ

In (11.1), the first and second terms on the right side show the Tauc-Lorentz and Drude contributions, respectively. As confirmed from this equation, a single Tauc-Lorentz peak is expressed by four parameters: i.e., the amplitude parameter Aj,

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broadening parameter Cj, peak transition energy E0,j, and optical gap Eg,j of the jth Tauc-Lorentz peak (see Fig. 1.9). On the other hand, the Drude contribution can also be described by the amplitude parameter AD and broadening parameter Γ. From the Drude parameters of (AD, Γ), the optical carrier concentration (Nopt) and optical mobility (μopt) can be estimated further if the effective mass m* is known (see Sect. 18.3.3 in Vol. 1). In general, Nopt shows quite good agreement with the carrier concentration obtained from Hall measurements (NHall), while μopt is generally larger than μHall (Sect. 18.4 in Vol. 1). Since the free carrier absorption increases significantly with Nopt and NHall, the values of (Nopt, μopt) and (NHall, μHall) are described whenever possible. For SnO2:F, In2O3:Sn and doped ZnO in this chapter, the calculation of (Nopt, μopt) from (AD, Γ) was performed using (18.24)–(18.25) in Vol. 1 and the result of Table 18.1 in Vol. 1 by taking the effect of nonparabolic TCO conduction band into account. In this chapter, the carrier concentration of various TCO materials is basically represented by NHall, as the calculation of Nopt is not possible when m* is unknown. Using the parameters of (11.1), ε1(E) can then be calculated from the Kramers-Kronig integration of each Tauc-Lorentz ε2 peak and the ε1 contribution of the Drude term: 0 2 B ε1 ðEÞ = ∑ @ε1, j ð∞Þ + P π j=1 m

Z∞ Eg

1 ′

′

E ε2, j ðE Þ ′C AD dE A − 2 , E ′2 − E 2 E + Γ2

ð11:2Þ

where ε1,j(∞) represents a constant contribution to ε1(E) at high energies. The first term on the right side shows the Kramers-Kronig integration of the jth Tauc-Lorentz peak [ε2,j(E′) in (11.2)] and this integration can be performed rather easily using the exact equations shown in (1.20). As confirmed from (11.2), when a dielectric function is modeled by combining several Tauc-Lorentz peaks, ε1(E) is calculated as a sum of the ε1 contributions obtained from each Tauc-Lorentz peak (see the example of graphene in Fig. 11.1). The calculation example of the Tauc-Lorentz model is also given by (1.26). On the other hand, the second term on the right side of (11.2) represents the ε1 contribution of the Drude model (Sects. 5.3.4 in Vol. 1 and 18.2.3 in Vol. 1). A free software described in Sect. 2.7 can further be applied to calculate the dielectric function from the Tauc-Lorentz and Drude parameters listed in this chapter. In the actual ε1(E) and ε2(E) calculation, however, E should be chosen so that |E − Eg| in (1.20) does not become zero. The parameterization of all the TCO dielectric functions using (11.1) and (11.2), described in this chapter, was implemented by the group of Gifu University (A. Nakane, S. Fujimoto, and M. Tamakoshi), unless otherwise noted.

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Optical Data of Transparent Conductive Oxides

11.2.1 Graphene Data from M. Losurdo, M. M. Giangregorio, G. V. Bianco, P. Capezzuto, G. Bruno [2]. The optical data have been extracted from chemical-vapor-deposited monolayer graphene (polycrystal) on glass substrate. This graphene layer shows p-type conductivity with NHall = 6 × 1011 cm−2 and μHall = 1200 cm2/(Vs) (Fig. 11.1, Tables 11.1 and 11.2).

Fig. 11.1 Dielectric function of graphene at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.1 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for graphene

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 Drude

41.068

0.819

0.435

0.174

1.777

22.262

3.360

1.706

0.071

0

12.222

3.205

3.801

1 × 10−4

0

11.461

1.330

4.278

0.319

0

14.500

0.613

4.614

2.232

0

6.155

0.230

–

–

–

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Table 11.2 Optical constants of graphene calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.012 3.035 3.049 3.055 3.053 3.046 3.035 3.022 3.007 2.992 2.977 2.962 2.948 2.934 2.921 2.909 2.897 2.886 2.876 2.866 2.857 2.839 2.824 2.809 2.796 2.784 2.772 2.762 2.753 2.745 2.738 2.732 2.727 2.723

2.257 2.169 2.084 2.006 1.935 1.872 1.816 1.767 1.724 1.688 1.656 1.628 1.604 1.583 1.565 1.549 1.535 1.523 1.512 1.503 1.495 1.482 1.474 1.468 1.465 1.466 1.468 1.472 1.479 1.487 1.496 1.507 1.519 1.532

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.720 2.717 2.716 2.715 2.715 2.716 2.718 2.720 2.723 2.726 2.730 2.735 2.740 2.745 2.751 2.757 2.763 2.770 2.777 2.784 2.792 2.800 2.807 2.816 2.824 2.832 2.841 2.849 2.858 2.867 2.876 2.885 2.894 2.903

1.546 1.561 1.577 1.592 1.609 1.625 1.642 1.660 1.677 1.695 1.712 1.730 1.748 1.766 1.783 1.801 1.819 1.836 1.854 1.871 1.888 1.905 1.922 1.939 1.956 1.973 1.989 2.006 2.022 2.038 2.054 2.070 2.086 2.102

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.912 2.921 2.931 2.940 2.949 2.959 2.968 2.977 2.987 2.996 3.005 3.015 3.024 3.034 3.043 3.052 3.062 3.071 3.081 3.090 3.100 3.109 3.118 3.128 3.137 3.147 3.156 3.166 3.175 3.185 3.194 3.204 3.213

2.118 2.133 2.149 2.164 2.179 2.195 2.210 2.225 2.240 2.254 2.269 2.284 2.299 2.313 2.328 2.342 2.356 2.371 2.385 2.399 2.413 2.427 2.441 2.455 2.469 2.483 2.497 2.510 2.524 2.538 2.551 2.565 2.578

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11.2.2 In2O3 (Non-doped) Data: unpublished results of T. Koida. The preparation and characterization of In2O3 layers can be found in [3]. The optical data have been extracted from a polycrystalline In2O3 layer formed by rf sputtering at room temperature using an Ar/O2 gas mixture and an In2O3 target. The electrical characteristics of this layer are NHall = 5.3 × 1018 cm−3 and μHall = 13.2 cm2/(Vs) (Tables 11.3, 11.4 and Fig. 11.2).

Fig. 11.2 Dielectric function of non-doped In2O3 at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 11.3 Tanc-Lorentz parameters of (8.1) and (8.2) for non-doped In2O3

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

0.263 9.740 22.790 93.634

0.706 0.463 1.707 1.459

2.855 3.865 4.163 6.986

1.823 3.260 2.773 4.191

1.489 0 0 0

= = = =

1 2 3 4

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Table 11.4 Optical constants of non-doped In2O3 calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.323 2.345 2.371 2.400 2.428 2.444 2.445 2.435 2.419 2.400 2.382 2.363 2.346 2.329 2.314 2.299 2.285 2.272 2.260 2.248 2.238 2.218 2.202 2.188 2.175 2.165 2.155 2.146 2.138 2.130 2.123 2.117 2.111 2.105

0.398 0.390 0.378 0.357 0.323 0.279 0.232 0.190 0.157 0.130 0.109 9.17 × 7.74 × 6.56 × 5.57 × 4.76 × 4.08 × 3.52 × 3.04 × 2.65 × 2.32 × 1.84 × 1.52 × 1.28 × 1.09 × 9.43 × 7.88 × 6.36 × 5.03 × 3.94 × 3.07 × 2.39 × 1.86 × 1.45 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.100 2.095 2.091 2.087 2.083 2.080 2.076 2.073 2.070 2.068 2.065 2.063 2.060 2.058 2.056 2.054 2.052 2.051 2.049 2.047 2.046 2.044 2.043 2.042 2.041 2.039 2.038 2.037 2.036 2.035 2.034 2.033 2.032 2.031

1.13 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.031 2.030 2.029 2.028 2.028 2.027 2.026 2.026 2.025 2.024 2.024 2.023 2.023 2.022 2.022 2.021 2.021 2.020 2.020 2.019 2.019 2.018 2.018 2.018 2.017 2.017 2.017 2.016 2.016 2.016 2.015 2.015 2.015

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

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11.2.3 In2O3:H (NHall = 2.1 × 1020 cm−3) Data from T. Koida, M. Kondo, K. Tsutsumi, A. Sakaguchi, M. Suzuki and H. Fujiwara [4] [see also Fig. 19.9 (poly-In2O3:H) in Chap. 19 (Vol. 1)]. The optical data have been extracted from a high-mobility In2O3:H polycrystal formed by a two-step process: (i) rf sputtering at room temperature using an In2O3 target and an Ar/O2 gas mixture with H2O vapor and (ii) thermal annealing at 200 °C. The electrical characteristics of this layer are NHall = 2.1 × 1020 cm−3 and μHall = 108 cm2/(Vs) with Nopt = 1.85 × 1020 cm−3 and μopt = 104 cm2/(Vs) (Table 19.2 in Vol. 1) (Tables 11.5, 11.6 and Fig. 11.3).

Fig. 11.3 Dielectric function of In2O3:H at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.5 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for In2O3:H

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 Drude

45.989

0.684

4.061

3.714

2.236

25.507

1.971

4.162

3.054

0

27.441

4.016

5.892

3.285

0

10.891

0.436

7.095

3.069

0

0.759

0.033

–

–

–

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503

Table 11.6 Optical constants of In2O3:H calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.436 2.450 2.449 2.435 2.413 2.388 2.364 2.342 2.323 2.305 2.288 2.272 2.256 2.241 2.226 2.212 2.199 2.187 2.176 2.165 2.155 2.138 2.124 2.112 2.101 2.091 2.082 2.074 2.067 2.060 2.054 2.048 2.042 2.037

0.357 0.303 0.247 0.198 0.158 0.127 0.104 8.66 × 7.19 × 5.88 × 4.73 × 3.73 × 2.88 × 2.17 × 1.58 × 1.12 × 7.61 × 4.84 × 2.79 × 1.37 × 5.33 × 2.12 × 2.29 × 2.47 × 2.66 × 2.86 × 3.07 × 3.29 × 3.52 × 3.75 × 4.00 × 4.26 × 4.52 × 4.80 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.032 2.027 2.023 2.018 2.014 2.010 2.006 2.002 1.999 1.995 1.991 1.988 1.985 1.981 1.978 1.975 1.972 1.969 1.966 1.963 1.960 1.957 1.954 1.951 1.948 1.945 1.942 1.939 1.936 1.933 1.930 1.927 1.925 1.922

5.09 5.39 5.70 6.03 6.36 6.71 7.07 7.45 7.83 8.23 8.65 9.07 9.52 9.97 1.04 1.09 1.14 1.19 1.25 1.30 1.36 1.42 1.48 1.54 1.60 1.67 1.73 1.80 1.87 1.94 2.02 2.09 2.17 2.25

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.919 1.916 1.913 1.910 1.907 1.904 1.901 1.898 1.895 1.892 1.889 1.886 1.883 1.880 1.877 1.874 1.871 1.868 1.865 1.861 1.858 1.855 1.852 1.849 1.845 1.842 1.839 1.835 1.832 1.828 1.825 1.822 1.818

2.33 2.42 2.50 2.59 2.68 2.77 2.87 2.97 3.07 3.17 3.27 3.38 3.49 3.60 3.71 3.83 3.95 4.07 4.19 4.32 4.45 4.58 4.72 4.86 5.00 5.14 5.29 5.44 5.59 5.75 5.91 6.07 6.24

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

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11.2.4 In2O3:Sn (NHall = 4.9 × 1020 cm−3) Data from H. Fujiwara and M. Kondo [5]. The optical data have been extracted from an ITO layer formed by rf sputtering at room temperature using an Ar gas and an ITO target (In2O3:SnO2 = 90:10 wt.%). The electrical characteristics of this layer are NHall = 4.9 × 1020 cm−3 and μHall = 23.0 cm2/(Vs) with Nopt = 4.6 × 1020 cm−3 and μopt = 23.7 cm2/(Vs) (Tables 11.7, 11.8 and Fig. 11.4).

Fig. 11.4 Dielectric function of In2O3:Sn (NHall = 4.9 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.7 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for In2O3:Sn (NHall = 4.9 × 1020 cm−3)

Model TL peak1 TL peak2 TL peak3 Drude

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

2.247

0.684

3.410

2.389

3.253

20.530

0.689

3.672

3.184

0

127.242

1.583

3.753

3.596

0

1.909

0.147

–

–

–

A/AD (eV)

11

Transparent Conductive Oxides

505

Table 11.8 Optical constants of In2O3:Sn (NHall = 4.9 × 1020 cm−3). The optical data reported by Fujiwara et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.386 2.386 2.381 2.373 2.361 2.347 2.330 2.309 2.284 2.267 2.251 2.235 2.222 2.208 2.194 2.179 2.168 2.156 2.145 2.135 2.126 2.110 2.096 2.084 2.076 2.069 2.062 2.055 2.048 2.041 2.035 2.029 2.023 2.018

0.347 0.327 0.306 0.283 0.261 0.237 0.214 0.189 0.164 0.145 0.128 0.112 9.65 × 8.40 × 7.34 × 5.89 × 5.13 × 4.32 × 3.61 × 3.02 × 2.55 × 1.81 × 1.32 × 1.01 × 8.13 × 6.58 × 5.44 × 4.68 × 4.29 × 4.26 × 4.51 × 4.80 × 5.10 × 5.42 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.013 2.007 2.002 1.997 1.992 1.987 1.982 1.977 1.972 1.967 1.962 1.957 1.952 1.946 1.941 1.936 1.931 1.926 1.921 1.915 1.910 1.905 1.899 1.894 1.888 1.883 1.877 1.871 1.865 1.860 1.854 1.848 1.842 1.836

5.74 6.09 6.44 6.81 7.19 7.59 8.00 8.42 8.87 9.32 9.80 1.03 1.08 1.13 1.19 1.24 1.30 1.36 1.42 1.49 1.55 1.62 1.69 1.76 1.84 1.91 1.99 2.08 2.16 2.25 2.33 2.43 2.52 2.62

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.830 1.823 1.817 1.811 1.804 1.798 1.791 1.784 1.778 1.771 1.764 1.757 1.750 1.743 1.736 1.728 1.721 1.714 1.706 1.698 1.691 1.683 1.675 1.667 1.659 1.650 1.642 1.634 1.625 1.616 1.608 1.599 1.590

2.72 2.82 2.93 3.03 3.14 3.26 3.38 3.50 3.62 3.75 3.88 4.02 4.15 4.30 4.44 4.59 4.75 4.90 5.07 5.24 5.40 5.58 5.76 5.95 6.14 6.33 6.53 6.74 6.95 7.17 7.39 7.62 7.85

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

506

A. Nakane et al.

11.2.5 In2O3:Sn (NHall = 7.2 × 1020 cm−3) Data from H. Fujiwara and M. Kondo [5]. The optical data have been extracted from an ITO layer formed by rf sputtering at 200 °C using an Ar gas and an ITO target (In2O3:SnO2 = 90:10 wt.%). The electrical characteristics of this layer are NHall = 7.2 × 1020 cm−3 and μHall = 43.4 cm2/(Vs) with Nopt = 7.0 × 1020 cm−3 and μopt = 22.9 cm2/(Vs) (Tables 11.9, 11.10 and Fig. 11.5).

Fig. 11.5 Dielectric function of In2O3:Sn (NHall = 7.2 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.9 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for In2O3:Sn (NHall = 7.2 × 1020 cm−3)

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 Drude

12.267

1.159

4.635

3.059

2.275

73.547

4.751

6.042

3.579

0

2.620

0.137

–

–

–

11

Transparent Conductive Oxides

507

Table 11.10 Optical constants of In2O3:Sn (NHall = 7.2 × 1020 cm−3). The optical data reported by Fujiwara et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.335 2.312 2.290 2.269 2.250 2.233 2.213 2.192 2.173 2.161 2.148 2.136 2.126 2.116 2.106 2.095 2.088 2.079 2.071 2.064 2.057 2.043 2.030 2.018 2.007 1.997 1.987 1.977 1.968 1.959 1.950 1.942 1.933 1.925

0.141 0.115 9.32 × 7.46 × 5.89 × 4.50 × 3.33 × 2.48 × 1.77 × 1.40 × 1.06 × 9.26 × 7.54 × 7.09 × 6.30 × 4.57 × 4.57 × 3.51 × 3.23 × 2.22 × 2.71 × 2.44 × 3.43 × 3.70 × 3.99 × 4.29 × 4.61 × 4.94 × 5.28 × 5.64 × 6.02 × 6.42 × 6.83 × 7.26 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.917 1.909 1.901 1.894 1.886 1.878 1.871 1.863 1.855 1.848 1.840 1.833 1.825 1.817 1.809 1.802 1.794 1.786 1.778 1.770 1.762 1.754 1.745 1.737 1.729 1.720 1.712 1.703 1.694 1.685 1.676 1.667 1.658 1.648

7.71 8.18 8.67 9.18 9.71 1.03 1.08 1.14 1.20 1.27 1.34 1.40 1.48 1.55 1.63 1.71 1.79 1.88 1.97 2.06 2.15 2.25 2.35 2.46 2.57 2.68 2.80 2.92 3.04 3.17 3.30 3.44 3.58 3.73

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.639 1.629 1.620 1.610 1.600 1.590 1.579 1.569 1.559 1.548 1.537 1.526 1.515 1.503 1.492 1.480 1.469 1.457 1.444 1.432 1.419 1.407 1.394 1.380 1.367 1.353 1.340 1.326 1.311 1.297 1.282 1.267 1.252

3.88 × 4.04 × 4.20 × 4.37 × 4.54 × 4.72 × 4.90 × 5.09 × 5.29 × 5.49 × 5.70 × 5.92 × 6.14 × 6.38 × 6.62 × 6.87 × 7.12 × 7.39 × 7.66 × 7.95 × 8.24 × 8.55 × 8.86 × 9.20 × 9.53 × 9.89 × 0.103 0.106 0.110 0.114 0.119 0.123 0.128

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

508

A. Nakane et al.

11.2.6 In2O3:Sn (NHall = 1.2 × 1021 cm−3) Data from H. Fujiwara and M. Kondo [5] (see also Fig. 18.14 in Vol. 1). The optical data have been extracted from an ITO layer formed by rf sputtering at 240 °C using an Ar gas and an ITO target (In2O3:SnO2 = 90:10 wt%). The electrical characteristics of this layer are NHall = 1.2 × 1021 cm−3 and μHall = 31 cm2/(Vs) with Nopt = 1.2 × 1021 cm−3 and μopt = 27.0 cm2/(Vs) (Tables 11.11, 11.12 and Fig. 11.6).

Fig. 11.6 Dielectric function of In2O3:Sn (NHall = 1.2 × 1021 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.11 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for In2O3:Sn (NHall = 1.2 × 1021 cm−3)

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 Drude

53.445

1.741

4.580

3.731

2.635

18.514

1.534

6.039

2.761

0

3.786

0.102

–

–

–

11

Transparent Conductive Oxides

509

Table 11.12 Optical constants of In2O3:Sn (NHall = 1.2 × 1021 cm−3). The optical data reported by Fujiwara et al. are shown λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.309 2.287 2.263 2.234 2.207 2.186 2.168 2.151 2.133 2.120 2.108 2.096 2.085 2.074 2.065 2.053 2.045 2.036 2.027 2.020 2.012 1.996 1.983 1.970 1.958 1.947 1.936 1.925 1.915 1.904 1.894 1.884 1.874 1.864

9.95 7.69 5.66 3.93 3.29 2.86 2.51 2.14 1.80 1.55 1.34 1.25 1.16 1.07 9.54 8.25 7.35 6.45 6.25 5.96 5.85 6.00 3.77 4.08 4.39 4.73 5.08 5.44 5.83 6.24 6.66 7.11 7.57 8.06

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.854 1.844 1.834 1.824 1.815 1.805 1.794 1.784 1.774 1.764 1.753 1.743 1.732 1.721 1.710 1.699 1.688 1.676 1.665 1.653 1.641 1.629 1.617 1.604 1.591 1.579 1.565 1.552 1.538 1.524 1.510 1.496 1.481 1.466

8.57 9.10 9.66 1.02 1.08 1.15 1.21 1.28 1.36 1.43 1.51 1.59 1.67 1.76 1.85 1.95 2.05 2.15 2.26 2.37 2.49 2.61 2.73 2.87 3.00 3.14 3.29 3.45 3.61 3.77 3.95 4.13 4.32 4.52

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.451 1.435 1.420 1.404 1.387 1.370 1.353 1.336 1.318 1.299 1.281 1.261 1.242 1.222 1.201 1.180 1.158 1.136 1.114 1.090 1.066 1.041 1.016 0.990 0.963 0.935 0.906 0.876 0.846 0.814 0.782 0.748 0.713

4.72 × 4.94 × 5.16 × 5.40 × 5.64 × 5.90 × 6.17 × 6.45 × 6.75 × 7.06 × 7.38 × 7.72 × 8.09 × 8.47 × 8.87 × 9.30 × 9.75 × 0.102 0.107 0.113 0.119 0.125 0.131 0.139 0.146 0.155 0.164 0.174 0.185 0.197 0.211 0.226 0.243

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

510

A. Nakane et al.

11.2.7 InZnO (NHall = 2.5 × 1020 cm−3) Data: unpublished results of T. Koida. The optical data have been extracted from an amorphous InZnO layer (non-doped) formed by rf sputtering at room temperature using an Ar/O2 gas mixture and an InZnO target (In2O3:ZnO = 90.6:9.4 wt.%) [6]. The electrical characteristics of this layer are NHall = 2.5 × 1020 cm−3 and μHall = 50.4 cm2/(Vs) (Fig. 19.4b in Vol. 1) (Tables 11.13, 11.14 and Fig. 11.7).

Fig. 11.7 Dielectric function of InZnO (NHall = 2.5 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.13 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for InZnO (NHall = 2.5 × 1020 cm−3)

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 Drude

18.352

1.719

3.893

2.410

0.892

0.992

0.979

4.561

0.766

0

56.582

1.250

7.483

2.874

0

1.099

0.081

–

–

–

11

Transparent Conductive Oxides

511

Table 11.14 Optical constants of InZnO (NHall = 2.5 × 1020 cm−3) calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.389 2.402 2.413 2.424 2.433 2.440 2.445 2.448 2.449 2.447 2.443 2.437 2.430 2.421 2.412 2.401 2.391 2.379 2.368 2.357 2.345 2.323 2.301 2.280 2.260 2.242 2.225 2.209 2.194 2.181 2.168 2.156 2.146 2.136

0.453 0.437 0.419 0.400 0.379 0.357 0.333 0.310 0.286 0.262 0.240 0.218 0.197 0.178 0.160 0.144 0.129 0.115 0.103 9.19 × 8.17 × 6.44 × 5.04 × 3.94 × 3.06 × 2.36 × 1.82 × 1.41 × 1.10 × 8.80 × 7.39 × 6.64 × 6.37 × 6.19 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.127 2.119 2.111 2.103 2.096 2.090 2.083 2.077 2.071 2.065 2.059 2.054 2.048 2.043 2.038 2.033 2.028 2.023 2.018 2.014 2.009 2.004 2.000 1.995 1.991 1.986 1.982 1.978 1.973 1.969 1.964 1.960 1.956 1.951

6.04 5.91 5.80 5.71 5.64 5.59 5.55 5.53 5.53 5.54 5.56 5.59 5.63 5.69 5.75 5.83 5.92 6.02 6.12 6.24 6.37 6.50 6.65 6.80 6.96 7.14 7.32 7.51 7.70 7.91 8.13 8.35 8.59 8.83

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.947 1.943 1.938 1.934 1.930 1.925 1.921 1.916 1.912 1.907 1.903 1.898 1.894 1.889 1.885 1.880 1.876 1.871 1.866 1.862 1.857 1.852 1.848 1.843 1.838 1.833 1.828 1.823 1.818 1.813 1.808 1.803 1.798

9.08 9.35 9.62 9.90 1.02 1.05 1.08 1.11 1.14 1.18 1.21 1.25 1.28 1.32 1.36 1.40 1.44 1.48 1.53 1.57 1.62 1.66 1.71 1.76 1.81 1.86 1.91 1.97 2.02 2.08 2.13 2.19 2.25

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

512

A. Nakane et al.

11.2.8 MoOx Data: unpublished results of S. Fujimoto. The optical data have been extracted from an amorphous MoOx layer (x = 2–3) formed by rf sputtering at room temperature using an Ar/O2 gas mixture and a Mo target. The results obtained by varying the Ar/O2 flow ratio are shown (Tables 11.15, 11.16, 11.17, 11.18 and Fig. 11.8).

Fig. 11.8 Dielectric function of MoOx layers at room temperature. The results for MoOx layers prepared using different Ar/O2 flow ratios are shown. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 11.15 Tauc-Lorentz parameters of (8.1) and (8.2) for MoOx (Ar/O2 = 4)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2

100.142 43.743

3.008 0.239

3.994 11.570

2.808 4.051

0.791 0

Table 11.16 Tauc-Lorentz parameters of (8.1) and (8.2) for MoOx (Ar/O2 = 27)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2 j=3

1.250 98.965 76.640

0.870 3.037 0.254

1.320 4.065 12.474

0.469 2.817 5.445

0.436 0 0

11

Transparent Conductive Oxides

513

Table 11.17 Optical constants of MoOx (Ar/O2 = 4). The optical data obtained by S. Fujimoto are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.487 2.519 2.543 2.561 2.573 2.586 2.590 2.593 2.592 2.589 2.582 2.573 2.562 2.549 2.532 2.515 2.497 2.481 2.464 2.446 2.431 2.398 2.370 2.344 2.319 2.299 2.278 2.260 2.248 2.236 2.222 2.213 2.203 2.195

0.663 0.63 0.593 0.554 0.511 0.467 0.427 0.386 0.348 0.309 0.278 0.244 0.215 0.185 0.159 0.133 0.112 0.095 0.077 0.062 0.05 0.028 0.013 0.005 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.187 2.180 2.175 2.169 2.163 2.159 2.154 2.150 2.146 2.142 2.139 2.135 2.134 2.129 2.127 2.125 2.122 2.120 2.118 2.116 2.114 2.112 2.110 2.109 2.108 2.105 2.104 2.103 2.102 2.100 2.099 2.098 2.098 2.097

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.004 0.004 0.005 0.004 0.004

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.0956 2.0954 2.0943 2.0944 2.0932 2.0912 2.0901 2.0918 2.0899 2.0901 2.0890 2.0893 2.0899 2.0877 2.0872 2.0852 2.0868 2.0845 2.0855 2.0847 2.0840 2.0839 2.0846 2.0838 2.0838 2.0830 2.0821 2.0813 2.0819 2.0816 2.0823 2.0805 2.0794

0.005 0.004 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.006 0.005 0.005 0.005 0.006 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.002 0.002

514

A. Nakane et al.

Table 11.18 Optical constants of MoOx (Ar/O2 = 27). The optical data obtained by S. Fujimoto are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.505 2.530 2.554 2.564 2.581 2.586 2.589 2.589 2.584 2.576 2.571 2.560 2.551 2.536 2.519 2.500 2.483 2.468 2.450 2.432 2.415 2.384 2.353 2.326 2.300 2.277 2.256 2.238 2.220 2.210 2.193 2.183 2.173 2.164

0.655 0.615 0.577 0.538 0.494 0.454 0.414 0.375 0.338 0.301 0.271 0.238 0.213 0.184 0.159 0.135 0.115 0.099 0.083 0.069 0.056 0.037 0.024 0.019 0.016 0.018 0.015 0.016 0.018 0.019 0.021 0.022 0.023 0.025

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.155 2.146 2.139 2.133 2.127 2.121 2.116 2.111 2.106 2.103 2.100 2.096 2.094 2.091 2.089 2.088 2.086 2.086 2.085 2.086 2.086 2.086 2.088 2.088 2.090 2.092 2.094 2.096 2.099 2.102 2.105 2.107 2.111 2.115

0.027 0.028 0.031 0.034 0.036 0.040 0.043 0.046 0.051 0.053 0.058 0.061 0.067 0.069 0.073 0.077 0.081 0.085 0.089 0.093 0.097 0.101 0.104 0.108 0.111 0.115 0.118 0.121 0.123 0.126 0.128 0.129 0.130 0.132

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.117 2.121 2.124 2.127 2.131 2.134 2.136 2.143 2.146 2.147 2.148 2.155 2.160 2.159 2.160 2.164 2.168 2.170 2.173 2.176 2.178 2.180 2.183 2.185 2.188 2.188 2.190 2.191 2.192 2.195 2.196 2.196 2.197

0.133 0.134 0.135 0.135 0.136 0.136 0.136 0.134 0.134 0.133 0.133 0.132 0.131 0.130 0.129 0.127 0.126 0.124 0.123 0.121 0.118 0.116 0.114 0.111 0.108 0.106 0.104 0.101 0.098 0.095 0.092 0.089 0.086

11

Transparent Conductive Oxides

515

11.2.9 NiO Data from H. L. Lu, G. Scarel, M. Alia, M. Fanciulli, S.-J. Ding and D. W. Zhang [7]. The optical data have been extracted from an as-deposited NiO layer prepared by atomic layer deposition using Ni(C5H5)2 and O3 sources at 300 °C (Tables 11.19, 11.20 and Fig. 11.9).

Fig. 11.9 Dielectric function of NiO at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 11.19 Tauc-Lorentz parameters of (8.1) and (8.2) for NiO. The model parameters reported by Lu et al. are summarized Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2

111.89 59.10

0.82 5.83

3.96 5.09

3.30 2.53

2.50 0

516

A. Nakane et al.

Table 11.20 Optical constants of NiO calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.852 2.954 3.040 3.101 3.130 3.130 3.109 3.072 3.029 2.983 2.937 2.894 2.855 2.819 2.786 2.758 2.734 2.714 2.695 2.678 2.662 2.632 2.606 2.581 2.559 2.538 2.519 2.501 2.484 2.470 2.457 2.447 2.437 2.428

1.086 1.014 0.916 0.800 0.677 0.559 0.455 0.367 0.297 0.242 0.199 0.166 0.141 0.122 0.108 9.73 × 8.87 × 8.05 × 7.27 × 6.53 × 5.82 × 4.54 × 3.43 × 2.48 × 1.70 × 1.07 × 5.94 × 2.60 × 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.420 2.413 2.406 2.400 2.394 2.389 2.384 2.380 2.375 2.371 2.368 2.364 2.361 2.358 2.355 2.352 2.349 2.347 2.344 2.342 2.340 2.338 2.336 2.334 2.332 2.330 2.329 2.327 2.326 2.324 2.323 2.322 2.320 2.319

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.318 2.317 2.316 2.315 2.314 2.313 2.312 2.311 2.310 2.309 2.309 2.308 2.307 2.306 2.306 2.305 2.304 2.304 2.303 2.302 2.302 2.301 2.301 2.300 2.300 2.299 2.299 2.298 2.298 2.297 2.297 2.296 2.296

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

11

Transparent Conductive Oxides

11.2.10

517

SnO2 (Non-doped)

Data from H. S. So, J.-W. Park, D. H. Jung, K. H. Ko and H. Lee [8]. The optical data have been extracted from a polycrystalline SnO layer, which is prepared by sputtering using an Ar gas and a non-doped SnO2 target, followed by thermal annealing at 800 °C. The electrical characteristics of this layer are NHall = 2.6 × 1019 cm−3 and μHall = 1.0 cm2/(Vs) (Tables 11.21, 11.22 and Fig. 11.10).

Fig. 11.10 Dielectric function of SnO2 (non-doped) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 11.21 Tauc-Lorentz parameters of (8.1) and (8.2) for SnO2 (non-doped)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

0.492 110.633 1.947 94.303

1.660 1.569 0.505 7.390

3.744 3.758 3.825 9.121

1.729 3.757 3.051 3.959

1.128 0 0 0

= = = =

1 2 3 4

518

A. Nakane et al.

Table 11.22 Optical constants of SnO2 (non-doped) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.277 2.268 2.257 2.246 2.234 2.220 2.206 2.195 2.183 2.172 2.161 2.152 2.143 2.134 2.127 2.120 2.113 2.107 2.102 2.096 2.091 2.082 2.074 2.067 2.060 2.054 2.049 2.044 2.039 2.035 2.031 2.027 2.024 2.021

0.138 0.117 9.93 × 8.38 × 7.01 × 5.79 × 4.88 × 4.18 × 3.52 × 2.99 × 2.57 × 2.25 × 2.00 × 1.79 × 1.62 × 1.47 × 1.35 × 1.23 × 1.14 × 1.05 × 9.67 × 8.32 × 7.16 × 6.17 × 5.31 × 4.57 × 3.94 × 3.40 × 2.93 × 2.52 × 2.17 × 1.86 × 1.60 × 1.37 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.018 2.015 2.012 2.010 2.008 2.005 2.003 2.001 2.000 1.998 1.996 1.995 1.993 1.992 1.991 1.989 1.988 1.987 1.986 1.985 1.984 1.983 1.982 1.981 1.980 1.980 1.979 1.978 1.977 1.977 1.976 1.976 1.975 1.974

1.17 × 10−3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.974 1.973 1.973 1.972 1.972 1.971 1.971 1.971 1.970 1.970 1.969 1.969 1.969 1.968 1.968 1.968 1.967 1.967 1.967 1.966 1.966 1.966 1.966 1.965 1.965 1.965 1.965 1.964 1.964 1.964 1.964 1.963 1.963

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

11

Transparent Conductive Oxides

11.2.11

519

SnO2:F (TEC-15)

Data from J. Chen, J. Li, C. Thornberry, M. N. Sestak, R. W. Collins, J. D. Walker, S. Marsillac, A. R. Aquino and A. Rockett [9]. The optical data of SnO2:F (TEC-15, Pilkington) have been extracted from a SnO2:F/SiO2/SnO2/glass structure (see also Sect. 18.5 in Vol. 1). The electrical characteristics of the SnO2:F layer (300 nm) have been reported to be NHall = 5.6 × 1020 cm−3 and μHall = 21 cm2/ (Vs) [10]. The Drude analysis of the SnO2:F dielectric function shown here leads to Nopt = 3.5 × 1020 cm−3 and μopt = 55.6 cm2/(Vs). The structure and electrical properties of TEC-8 are quite similar but a thicker SnO2:F layer (520 nm) is incorporated to lower sheet resistance (see Table 18.2 in Vol. 1) (Tables 11.23, 11.24 and Fig. 11.11).

Fig. 11.11 Room-temperature dielectric function of a SnO2:F layer incorporated into TEC-15. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.23 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for SnO2:F (TEC-15)

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 Drude

4.853

0.380

4.763

2.708

2.820

5.728

0.173

6.897

1 × 10−4

0

1.956

0.085

–

–

–

520

A. Nakane et al.

Table 11.24 Optical constants of SnO2:F (TEC-15) calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.173 2.153 2.136 2.121 2.107 2.095 2.084 2.075 2.066 2.057 2.049 2.042 2.035 2.029 2.023 2.017 2.012 2.007 2.002 1.997 1.993 1.984 1.976 1.968 1.961 1.954 1.948 1.942 1.936 1.930 1.924 1.918 1.913 1.907

3.68 3.02 2.52 2.15 1.86 1.63 1.44 1.29 1.17 1.06 9.75 9.01 8.39 7.85 7.39 7.00 6.66 6.37 6.12 5.90 5.72 5.44 5.24 5.12 5.06 5.05 5.09 5.14 5.22 5.30 5.40 5.51 5.63 5.77

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.902 1.896 1.891 1.886 1.880 1.875 1.870 1.864 1.859 1.854 1.848 1.843 1.837 1.832 1.826 1.821 1.815 1.810 1.804 1.798 1.792 1.786 1.780 1.774 1.768 1.762 1.756 1.750 1.743 1.737 1.730 1.724 1.717 1.710

5.91 6.07 6.24 6.43 6.62 6.83 7.05 7.28 7.52 7.77 8.04 8.32 8.61 8.92 9.24 9.57 9.91 1.03 1.06 1.10 1.14 1.18 1.23 1.27 1.32 1.37 1.42 1.47 1.52 1.57 1.63 1.69 1.75 1.81

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.703 1.696 1.689 1.682 1.675 1.668 1.660 1.653 1.645 1.638 1.630 1.622 1.614 1.606 1.598 1.589 1.581 1.572 1.564 1.555 1.546 1.537 1.528 1.518 1.509 1.499 1.490 1.480 1.470 1.460 1.450 1.439 1.429

1.87 1.94 2.01 2.08 2.15 2.23 2.30 2.38 2.46 2.55 2.63 2.72 2.81 2.91 3.01 3.11 3.21 3.32 3.42 3.54 3.65 3.77 3.90 4.02 4.15 4.29 4.43 4.57 4.72 4.87 5.03 5.19 5.35

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

11

Transparent Conductive Oxides

11.2.12

521

TiO2 (Polycrystal)

Data from M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, S. Fujimoto, M. Chikamatsu and H. Fujiwara [11]. The optical data have been extracted from a polycrystalline TiO2 (anataze) layer formed by a spray pyrolysis method at 450 °C. This TiO2 polycrystal shows isotropic optical properties (Tables 11.25, 11.26 and Fig. 11.12).

Fig. 11.12 Dielectric function of polycrystalline TiO2 (anatase) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 11.25 Tauc-Lorentz parameters of (8.1) and (8.2) for polycrystalline TiO2 (anatase). The model parameters reported by Shirayama et al. are summarized

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

94.341 177.870 28.662 153.220

0.693 1.127 1.028 11.861

3.904 4.359 5.514 8.603

3.215 3.636 4.894 4.950

0.537 0 0 0

= = = =

1 2 3 4

522

A. Nakane et al.

Table 11.26 Optical constants of polycrystalline TiO2 (anatase) calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.119 3.174 3.233 3.286 3.316 3.315 3.282 3.227 3.161 3.093 3.028 2.966 2.910 2.859 2.813 2.772 2.736 2.704 2.677 2.653 2.631 2.595 2.563 2.537 2.514 2.493 2.475 2.459 2.445 2.432 2.420 2.409 2.399 2.390

1.050 0.976 0.888 0.779 0.650 0.516 0.390 0.285 0.203 0.142 9.61 × 6.27 × 3.90 × 2.26 × 1.16 × 4.86 × 1.24 × 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.381 2.373 2.366 2.359 2.353 2.347 2.342 2.337 2.332 2.327 2.323 2.319 2.315 2.312 2.308 2.305 2.302 2.299 2.296 2.294 2.291 2.289 2.286 2.284 2.282 2.280 2.278 2.276 2.275 2.273 2.271 2.270 2.268 2.267

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.265 2.264 2.263 2.262 2.260 2.259 2.258 2.257 2.256 2.255 2.254 2.253 2.252 2.251 2.250 2.250 2.249 2.248 2.247 2.247 2.246 2.245 2.245 2.244 2.243 2.243 2.242 2.241 2.241 2.240 2.240 2.239 2.239

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−3 10−3

11

Transparent Conductive Oxides

11.2.13

523

TiO2 (Anatase Single Crystal)

Data from G. E. Jellison, Jr., L. A. Boatner and J. D. Budai [12]. A TiO2 anataze single crystal shows uniaxial optical anisotropy and the optical data for the ordinary and extraordinary rays are summarized (Tables 11.27, 11.28, 11.29, 11.30 and Fig. 11.13).

Fig. 11.13 Dielectric function of a TiO2 anatase single crystal at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 11.27 Tauc-Lorentz parameters of (8.1) and (8.2) for the ordinary ray in TiO2 (anatase single crystal)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j

67.736 31.185 5.331 330.100

0.522 0.885 0.561 9.403

3.852 4.536 4.804 4.998

3.197 2.962 2.593 3.685

0.309 0 0 0

Table 11.28 Tauc-Lorentz parameters of (8.1) and (8.2) for the extraordinary ray in TiO2 (anatase single crystal)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2 j=3

172.533 17.915 424.332

0.573 1.325 5.651

4.157 5.079 7.775

3.545 2.542 5.918

0.018 0 0

= = = =

1 2 3 4

524

A. Nakane et al.

Table 11.29 Optical constants for the ordinary ray in TiO2 (anatase single crystal), calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.130 3.140 3.182 3.254 3.333 3.385 3.391 3.356 3.298 3.232 3.167 3.105 3.049 2.999 2.955 2.915 2.879 2.848 2.820 2.795 2.773 2.735 2.703 2.675 2.651 2.630 2.611 2.594 2.579 2.566 2.554 2.542 2.532 2.522

0.844 0.833 0.823 0.789 0.710 0.590 0.454 0.332 0.236 0.165 0.114 7.80 × 5.28 × 3.52 × 2.30 × 1.47 × 9.34 × 6.11 × 4.41 × 3.19 × 2.24 × 1.03 × 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.514 2.505 2.498 2.491 2.484 2.478 2.472 2.467 2.462 2.457 2.453 2.449 2.445 2.441 2.437 2.434 2.431 2.428 2.425 2.422 2.419 2.417 2.414 2.412 2.410 2.408 2.406 2.404 2.402 2.400 2.398 2.397 2.395 2.394

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.392 2.391 2.389 2.388 2.387 2.385 2.384 2.383 2.382 2.381 2.380 2.379 2.378 2.377 2.376 2.375 2.374 2.374 2.373 2.372 2.371 2.371 2.370 2.369 2.369 2.368 2.367 2.367 2.366 2.365 2.365 2.364 2.364

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3

11

Transparent Conductive Oxides

525

Table 11.30 Optical constants for the extraordinary ray in TiO2 (anatase single crystal), calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.478 3.525 3.490 3.408 3.310 3.213 3.124 3.046 2.979 2.921 2.873 2.833 2.800 2.770 2.744 2.720 2.699 2.679 2.662 2.645 2.630 2.602 2.578 2.557 2.538 2.521 2.506 2.492 2.479 2.468 2.458 2.448 2.440 2.432

0.975 0.731 0.514 0.348 0.231 0.152 0.101 6.77 × 4.74 × 3.57 × 3.00 × 2.67 × 2.37 × 2.09 × 1.85 × 1.63 × 1.43 × 1.26 × 1.10 × 9.53 × 8.24 × 6.07 × 4.34 × 2.98 × 1.93 × 1.14 × 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.425 2.418 2.412 2.406 2.400 2.395 2.391 2.386 2.382 2.378 2.374 2.371 2.367 2.364 2.361 2.358 2.355 2.353 2.350 2.348 2.346 2.344 2.342 2.340 2.338 2.336 2.334 2.333 2.331 2.330 2.328 2.327 2.326 2.324

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.323 2.322 2.321 2.320 2.319 2.318 2.317 2.316 2.315 2.314 2.313 2.312 2.311 2.310 2.310 2.309 2.308 2.308 2.307 2.306 2.306 2.305 2.304 2.304 2.303 2.303 2.302 2.302 2.301 2.301 2.300 2.300 2.299

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3

526

11.2.14

A. Nakane et al.

TiO2 (Rutile Single Crystal)

Data from G. E. Jellison, Jr., F. A. Modine, and L. A. Boatner [13]. A TiO2 rutile single crystal shows uniaxial optical anisotropy and the optical data for the ordinary and extraordinary rays are summarized (Tables 11.31, 11.32, 11.33, 11.34 and Fig. 11.14).

Fig. 11.14 Dielectric function of a TiO2 rutile single crystal at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]. The dotted lines show the extrapolated result obtained from the Tauc-Lorentz model

Table 11.31 Tauc-Lorentz parameters of (8.1) and (8.2) for the ordinary ray in TiO2 (rutile single crystal)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

44.205 237.420 32.207 94.318 407.216

0.575 0.462 1.152 1.225 1.635

3.888 3.952 4.562 5.381 6.036

2.898 3.542 2.928 4.281 5.942

1.444 0 0 0 0

Table 11.32 Tauc-Lorentz parameters of (8.1) and (8.2) for the extraordinary ray in TiO2 (rutile single crystal)

Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2 j=3

98.921 255.549 159.686

0.466 0.922 3.028

3.698 4.065 7.900

3.469 3.090 4.930

0.734 0 0

= = = = =

1 2 3 4 5

11

Transparent Conductive Oxides

527

Table 11.33 Optical constants for the ordinary ray in TiO2 (rutile single crystal), calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

3.202 3.454 3.720 3.926 4.023 4.017 3.946 3.843 3.732 3.625 3.529 3.447 3.375 3.311 3.253 3.202 3.155 3.113 3.075 3.040 3.009 2.953 2.906 2.867 2.834 2.806 2.781 2.759 2.739 2.722 2.706 2.691 2.678 2.666

1.842 1.808 1.669 1.424 1.129 0.851 0.624 0.452 0.329 0.242 0.183 0.140 0.108 8.21 × 6.24 × 4.70 × 3.50 × 2.56 × 1.83 × 1.27 × 8.36 × 2.86 × 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.655 2.645 2.635 2.626 2.618 2.611 2.604 2.597 2.591 2.585 2.579 2.574 2.569 2.565 2.560 2.556 2.552 2.549 2.545 2.542 2.538 2.535 2.532 2.530 2.527 2.525 2.522 2.520 2.518 2.515 2.513 2.511 2.510 2.508

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.506 2.504 2.503 2.501 2.500 2.498 2.497 2.495 2.494 2.493 2.492 2.490 2.489 2.488 2.487 2.486 2.485 2.484 2.483 2.482 2.481 2.481 2.480 2.479 2.478 2.477 2.477 2.476 2.475 2.474 2.474 2.473 2.473

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3

528

A. Nakane et al.

Table 11.34 Optical constants for the extraordinary ray in TiO2 (rutile single crystal), calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

4.061 4.255 4.394 4.475 4.506 4.498 4.460 4.395 4.304 4.198 4.089 3.984 3.890 3.806 3.729 3.659 3.594 3.536 3.483 3.434 3.391 3.321 3.264 3.217 3.176 3.140 3.109 3.082 3.057 3.035 3.015 2.997 2.980 2.965

2.239 2.023 1.779 1.525 1.281 1.053 0.844 0.655 0.492 0.362 0.264 0.192 0.141 0.101 6.94 × 4.56 × 2.79 × 1.53 × 6.89 × 2.00 × 0 0 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.951 2.938 2.926 2.915 2.905 2.895 2.886 2.878 2.870 2.863 2.856 2.849 2.843 2.837 2.832 2.827 2.822 2.817 2.813 2.808 2.804 2.800 2.797 2.793 2.790 2.787 2.784 2.781 2.778 2.775 2.773 2.770 2.768 2.765

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.763 2.761 2.759 2.757 2.755 2.753 2.752 2.750 2.748 2.747 2.745 2.744 2.742 2.741 2.739 2.738 2.737 2.736 2.734 2.733 2.732 2.731 2.730 2.729 2.728 2.727 2.726 2.725 2.724 2.723 2.723 2.722 2.721

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−3 10−3

11

Transparent Conductive Oxides

11.2.15

529

WO3

Data: unpublished results of J.A. Woollam Co., Inc. (Tables 11.35, 11.36 and Fig. 11.15).

Fig. 11.15 Dielectric function of WO3 at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 11.35 Tauc-Lorentz parameters of (8.1) and (8.2) for WO3 Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2 j=3

81.565 28.205 43.097

1.725 3.591 0.100

4.435 5.943 12.220

3.249 3.602 5.104

0.821 0 0

530

A. Nakane et al.

Table 11.36 Optical constants of WO3 obtained by J.A. Woollam Co., Inc λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.632 2.620 2.602 2.579 2.552 2.523 2.494 2.464 2.434 2.405 2.377 2.351 2.326 2.303 2.282 2.263 2.247 2.233 2.221 2.209 2.199 2.180 2.163 2.149 2.136 2.125 2.115 2.106 2.097 2.090 2.083 2.076 2.071 2.065

0.405 0.342 0.285 0.234 0.189 0.151 0.119 0.092 0.069 0.051 0.037 0.026 0.018 0.012 0.009 0.007 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.060 2.055 2.051 2.047 2.043 2.040 2.036 2.033 2.030 2.027 2.025 2.022 2.020 2.018 2.016 2.014 2.012 2.010 2.008 2.007 2.005 2.004 2.002 2.001 2.000 1.998 1.997 1.996 1.995 1.994 1.993 1.992 1.991 1.990

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.9891 1.9883 1.9875 1.9867 1.9859 1.9852 1.9845 1.9838 1.9832 1.9826 1.9819 1.9814 1.9808 1.9802 1.9797 1.9792 1.9787 1.9782 1.9777 1.9772 1.9768 1.9764 1.9759 1.9755 1.9751 1.9748 1.9744 1.9740 1.9737 1.9733 1.9730 1.9727 1.9723

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

11

Transparent Conductive Oxides

11.2.16

531

ZnO (Non-doped)

Data from T. Hara, T. Maekawa, S. Minoura, Y. Sago, S. Niki and H. Fujiwara [14]. The optical data have been extracted from a sputter-deposited ZnO layer (Tables 11.37, 11.38 and Fig. 11.16).

Fig. 11.16 Dielectric function of ZnO (non-doped) at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 11.37 Tauc-Lorentz parameters of (8.1) and (8.2) for ZnO (non-doped) Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2 j=3

50.215 35.907 61.700

0.887 0.369 12.953

3.308 3.334 7.212

3.171 2.961 2.806

1.830 0 0

532

A. Nakane et al.

Table 11.38 Optical constants of ZnO (non-doped). The optical data reported by Hara et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.036 2.042 2.050 2.059 2.068 2.079 2.091 2.105 2.122 2.144 2.172 2.209 2.257 2.314 2.369 2.401 2.400 2.375 2.338 2.301 2.269 2.214 2.174 2.145 2.123 2.104 2.088 2.077 2.065 2.055 2.048 2.041 2.035 2.029

0.398 0.397 0.397 0.397 0.398 0.399 0.401 0.405 0.410 0.415 0.420 0.422 0.415 0.390 0.341 0.263 0.184 0.120 7.52 × 4.65 × 2.80 × 1.02 × 3.13 × 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.024 2.019 2.015 2.011 2.007 2.004 2.001 1.998 1.995 1.992 1.99 1.987 1.985 1.983 1.981 1.979 1.977 1.976 1.974 1.973 1.971 1.97 1.969 1.967 1.966 1.965 1.964 1.963 1.962 1.961 1.96 1.959 1.958 1.957

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.956 1.956 1.955 1.954 1.954 1.953 1.952 1.952 1.951 1.950 1.950 1.949 1.949 1.948 1.948 1.947 1.947 1.947 1.946 1.946 1.945 1.945 1.944 1.944 1.944 1.943 1.943 1.943 1.942 1.942 1.942 1.941 1.941

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10−2 10−2 10−2 10−2 10−3

11

Transparent Conductive Oxides

11.2.17

533

ZnO:Ga (NHall = 1.1 × 1020 cm−3)

Data from H. Fujiwara and M. Kondo [5] (see also Fig. 18.8 in Vol. 1). The optical data have been extracted from a ZnO:Ga layer formed by dc sputtering at 170 °C using an Ar gas and a ZnO target (Ga2O3: 3.4 wt.%). The electrical characteristics of this layer are NHall = 1.1 × 1020 cm−3 and μHall = 15.7 cm2/(Vs) with Nopt = 1.5 × 1020 cm−3 and μopt = 26.1 cm2/(Vs) (Tables 11.39, 11.40 and Fig. 11.17).

Fig. 11.17 Dielectric function of ZnO:Ga (NHall = 1.1 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.39 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ZnO:Ga (NHall = 1.1 × 1020 cm−3)

Model TL peak1 TL peak2 Drude

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

9.975

0.799

3.662

2.534

2.889

55.423

2.327

3.875

3.198

0

0.852

0.183

–

–

–

A/AD (eV)

534

A. Nakane et al.

Table 11.40 Optical constants of ZnO:Ga (NHall = 1.1 × 1020 cm−3). The optical data reported by Fujiwara et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.046 2.061 2.079 2.100 2.123 2.152 2.182 2.209 2.233 2.256 2.272 2.274 2.269 2.257 2.241 2.219 2.203 2.185 2.169 2.154 2.139 2.113 2.092 2.074 2.060 2.047 2.034 2.023 2.014 2.005 1.998 1.991 1.984 1.978

0.448 0.447 0.444 0.440 0.433 0.422 0.407 0.378 0.341 0.304 0.263 0.222 0.182 0.149 0.121 9.53 × 7.82 × 6.32 × 5.22 × 4.22 × 3.56 × 2.45 × 1.70 × 1.16 × 7.73 × 4.21 × 2.37 × 2.09 × 2.23 × 2.38 × 2.54 × 2.71 × 2.88 × 3.06 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.973 1.967 1.962 1.957 1.953 1.948 1.944 1.939 1.935 1.931 1.928 1.924 1.920 1.916 1.913 1.909 1.906 1.902 1.899 1.896 1.892 1.889 1.886 1.883 1.879 1.876 1.873 1.870 1.866 1.863 1.860 1.857 1.854 1.851

3.24 3.43 3.63 3.84 4.05 4.27 4.50 4.74 4.99 5.24 5.51 5.78 6.06 6.35 6.65 6.96 7.27 7.60 7.94 8.29 8.64 9.01 9.39 9.78 1.02 1.06 1.10 1.14 1.19 1.23 1.28 1.33 1.38 1.43

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.847 1.844 1.841 1.838 1.834 1.831 1.828 1.825 1.821 1.818 1.815 1.812 1.808 1.805 1.801 1.798 1.795 1.791 1.788 1.784 1.781 1.777 1.774 1.770 1.767 1.763 1.760 1.756 1.752 1.748 1.745 1.741 1.737

1.48 1.53 1.59 1.64 1.70 1.76 1.82 1.88 1.94 2.01 2.07 2.14 2.21 2.28 2.35 2.43 2.50 2.58 2.65 2.74 2.82 2.90 2.98 3.07 3.16 3.25 3.34 3.44 3.53 3.63 3.73 3.83 3.94

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

11

Transparent Conductive Oxides

11.2.18

535

ZnO:Al (Nopt = 1.5 × 1020 cm−3)

Data from T. Hara, T. Maekawa, S. Minoura, Y. Sago, S. Niki and H. Fujiwara [14]. The optical data have been extracted from a sputter-deposited ZnO:Al layer. The electrical characteristics of this layer are Nopt = 1.5 × 1020 cm−3 and μopt = 41.9 cm2/(Vs) (Tables 11.41, 11.42 and Fig. 11.18).

Fig. 11.18 Dielectric function of ZnO:Al (Nopt = 1.5 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.41 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ZnO:Al (Nopt = 1.5 × 1020 cm−3) Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 Drude

45.155 20.531 0.850

0.937 3.849 0.114

3.663 4.139 –

3.087 2.702 –

2.816 0 –

536

A. Nakane et al.

Table 11.42 Optical constants of ZnO:Al (Nopt = 1.5 × 1020 cm−3). The optical data reported by Hara et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.111 2.125 2.139 2.156 2.174 2.194 2.221 2.245 2.262 2.273 2.277 2.271 2.260 2.245 2.225 2.204 2.183 2.165 2.148 2.132 2.118 2.093 2.072 2.056 2.042 2.026 2.014 2.003 1.994 1.986 1.978 1.971 1.964 1.958

0.492 0.498 0.501 0.491 0.475 0.454 0.422 0.383 0.338 0.287 0.240 0.196 0.156 0.122 9.55 × 7.19 × 5.56 × 4.40 × 3.48 × 2.76 × 2.17 × 1.38 × 8.81 × 5.29 × 2.69 × 9.56 × 1.22 × 1.31 × 1.40 × 1.50 × 1.60 × 1.70 × 1.81 × 1.92 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.952 1.947 1.941 1.936 1.931 1.927 1.922 1.918 1.913 1.909 1.905 1.901 1.897 1.893 1.890 1.886 1.882 1.879 1.875 1.872 1.868 1.865 1.861 1.858 1.854 1.851 1.847 1.844 1.841 1.837 1.834 1.831 1.827 1.824

2.04 2.16 2.29 2.42 2.55 2.69 2.84 2.99 3.15 3.31 3.48 3.65 3.83 4.01 4.20 4.40 4.60 4.81 5.03 5.25 5.48 5.71 5.95 6.20 6.46 6.72 6.99 7.27 7.55 7.84 8.14 8.45 8.77 9.10

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−4 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.821 1.817 1.814 1.810 1.807 1.803 1.800 1.797 1.793 1.790 1.786 1.783 1.779 1.775 1.772 1.768 1.765 1.761 1.757 1.754 1.750 1.746 1.742 1.739 1.735 1.731 1.727 1.723 1.719 1.715 1.711 1.707 1.703

9.43 9.77 1.01 1.05 1.08 1.12 1.16 1.20 1.24 1.28 1.33 1.37 1.41 1.46 1.51 1.55 1.60 1.65 1.70 1.75 1.81 1.86 1.92 1.97 2.03 2.09 2.15 2.21 2.28 2.34 2.41 2.47 2.54

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

11

Transparent Conductive Oxides

11.2.19

537

ZnO:Ga (NHall = 4.8 × 1020 cm−3)

Data from H. Fujiwara and M. Kondo [5] (see also Fig. 18.8 in Vol. 1). The optical data have been extracted from a ZnO:Ga layer formed by dc sputtering at 240 °C using an Ar gas and a ZnO target (Ga2O3: 3.4 wt.%). The electrical characteristics of this layer are NHall = 4.8 × 1020 cm−3 and μHall = 15.5 cm2/(Vs) with Nopt = 4.2 × 1020 cm−3 and μopt = 27.1 cm2/(Vs) (Tables 11.43, 11.44 and Fig. 11.19).

Fig. 11.19 Dielectric function of ZnO:Ga (NHall = 4.8 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.43 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ZnO:Ga (NHall = 4.8 × 1020 cm−3) Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 Drude

11.894 77.627 1.811

0.706 1.548 0.133

3.877 4.019 –

2.857 3.605 –

2.906 0 –

538

A. Nakane et al.

Table 11.44 Optical constants of ZnO:Ga (NHall = 4.8 × 1020 cm−3). The optical data reported by Fujiwara et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.098 2.129 2.161 2.196 2.222 2.240 2.242 2.231 2.212 2.195 2.178 2.158 2.140 2.122 2.105 2.087 2.073 2.060 2.048 2.037 2.027 2.007 1.992 1.979 1.967 1.956 1.946 1.937 1.928 1.919 1.911 1.904 1.896 1.889

0.426 0.412 0.39 0.359 0.317 0.267 0.218 0.172 0.132 0.104 8.13 × 6.35 × 4.95 × 3.88 × 3.13 × 2.23 × 1.77 × 1.35 × 1.02 × 7.73 × 6.20 × 3.49 × 2.35 × 2.54 × 2.74 × 2.95 × 3.16 × 3.39 × 3.62 × 3.87 × 4.13 × 4.40 × 4.68 × 4.98 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.882 1.875 1.869 1.862 1.856 1.850 1.843 1.837 1.831 1.825 1.819 1.813 1.807 1.801 1.795 1.789 1.783 1.777 1.771 1.765 1.759 1.753 1.747 1.741 1.735 1.729 1.722 1.716 1.710 1.703 1.697 1.690 1.684 1.677

5.28 5.60 5.93 6.28 6.63 7.01 7.39 7.79 8.21 8.64 9.09 9.55 1.00 1.05 1.10 1.16 1.21 1.27 1.33 1.39 1.45 1.51 1.58 1.65 1.72 1.79 1.87 1.95 2.03 2.11 2.20 2.28 2.37 2.47

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.670 1.663 1.656 1.649 1.642 1.635 1.628 1.621 1.614 1.606 1.599 1.591 1.583 1.576 1.568 1.560 1.552 1.544 1.536 1.527 1.519 1.510 1.502 1.493 1.484 1.475 1.466 1.457 1.447 1.438 1.428 1.419 1.409

2.56 2.66 2.76 2.87 2.97 3.09 3.20 3.32 3.44 3.56 3.69 3.82 3.96 4.09 4.24 4.38 4.54 4.69 4.85 5.02 5.18 5.36 5.54 5.72 5.91 6.11 6.31 6.52 6.73 6.95 7.17 7.40 7.64

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

11

Transparent Conductive Oxides

11.2.20

539

ZnO:Ga (NHall = 6.5 × 1020 cm−3)

Data from H. Fujiwara and M. Kondo [5] (see also Fig. 18.8 in Vol. 1). The optical data have been extracted from a ZnO:Ga layer formed by dc sputtering at 240 °C using an Ar gas and a ZnO target (Ga2O3: 5.7 wt.%). The electrical characteristics of this layer are NHall = 6.5 × 1020 cm−3 and μHall = 23.1 cm2/(Vs) with Nopt = 6.8 × 1020 cm−3 and μopt = 24.1 cm2/(Vs) (Tables 11.45, 11.46 and Fig. 11.20).

Fig. 11.20 Dielectric function of ZnO:Ga (NHall = 6.5 × 1020 cm−3) at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 11.45 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ZnO:Ga (NHall = 6.5 × 1020 cm−3)

Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 Drude

17.420

0.571

4.029

3.452

2.718

39.381

2.849

4.603

3.071

0

2.537

0.130

–

–

–

540

A. Nakane et al.

Table 11.46 Optical constants of ZnO:Ga (NHall = 6.5 × 1020 cm−3). The optical data reported by Fujiwara et al. are shown λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.161 2.190 2.212 2.220 2.212 2.196 2.175 2.153 2.131 2.113 2.096 2.079 2.064 2.049 2.036 2.018 2.009 1.998 1.988 1.980 1.970 1.956 1.942 1.930 1.918 1.907 1.897 1.887 1.878 1.869 1.860 1.851 1.843 1.835

0.377 0.340 0.290 0.236 0.185 0.143 0.113 8.90 × 7.00 × 5.50 × 4.28 × 3.35 × 2.59 × 2.01 × 1.51 × 1.13 × 9.16 × 6.75 × 5.32 × 3.99 × 3.30 × 3.05 × 3.30 × 3.56 × 3.84 × 4.13 × 4.43 × 4.75 × 5.09 × 5.44 × 5.80 × 6.19 × 6.59 × 7.01 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.827 1.819 1.811 1.803 1.796 1.788 1.780 1.773 1.765 1.757 1.750 1.742 1.734 1.726 1.718 1.710 1.702 1.694 1.686 1.678 1.670 1.661 1.653 1.644 1.636 1.627 1.618 1.609 1.600 1.591 1.582 1.572 1.563 1.553

7.44 7.90 8.37 8.86 9.38 9.91 1.05 1.10 1.16 1.23 1.29 1.36 1.43 1.50 1.58 1.66 1.74 1.82 1.91 2.00 2.09 2.19 2.29 2.39 2.50 2.61 2.72 2.84 2.96 3.09 3.22 3.36 3.50 3.64

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.543 1.533 1.523 1.513 1.503 1.492 1.481 1.471 1.459 1.448 1.437 1.425 1.414 1.402 1.390 1.377 1.365 1.352 1.339 1.326 1.313 1.299 1.286 1.271 1.257 1.243 1.228 1.213 1.197 1.182 1.166 1.150 1.133

3.79 × 3.95 × 4.11 × 4.28 × 4.45 × 4.63 × 4.81 × 5.00 × 5.20 × 5.40 × 5.61 × 5.83 × 6.06 × 6.30 × 6.54 × 6.79 × 7.06 × 7.33 × 7.61 × 7.90 × 8.21 × 8.52 × 8.85 × 9.19 × 9.55 × 9.92 × 0.103 0.107 0.111 0.116 0.12 0.125 0.13

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

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References 1. G. E. Jellison Jr., F. A. Modine, Appl. Phys. Lett. 69, 371 (1996); Erratum, Appl. Phys. Lett. 69, 2137 (1996) 2. M. Losurdo, M.M. Giangregorio, G.V. Bianco, P. Capezzuto, G. Bruno, Thin Solid Films 571, 389 (2014) 3. T. Koida, H. Fujiwara, M. Kondo, Jpn. J. Appl. Phys. 46, L685 (2007) 4. T. Koida, M. Kondo, K. Tsutsumi, A. Sakaguchi, M. Suzuki, H. Fujiwara, J. Appl. Phys. 107, 033514 (2010) 5. H. Fujiwara, M. Kondo, Phys. Rev. B 71, 075109 (2005) 6. T. Koida, H. Sai, H. Shibata, M. Kondo, Jpn. J. Appl. Phys. 53, 05FA08 (2014) 7. H.L. Lu, G. Scarel, M. Alia, M. Fanciulli, S.-J. Ding, D. W. Zhang, Appl. Phys. Lett. 92, 222907 (2008) 8. H.S. So, J.-W. Park, D.H. Jung, K.H. Ko, H. Lee, J. Appl. Phys. 118, 085303 (2015) 9. J. Chen, J. Li, C. Thornberry, M.N. Sestak, R.W. Collins, J.D. Walker, S. Marsillac, A.R. Aquino, A. Rockett, in Proceedings of the 34th IEEE PVSC (IEEE, New York, 2009), p. 1748 10. D.S. Bhachu, M.R. Waugh, K. Zeissler, W.R. Branford, I.P. Parkin, Chem. Eur. J. 17, 11613 (2011) 11. M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, S. Fujimoto, M. Chikamatsu, H. Fujiwara, Phys. Rev. Appl. 5, 014012 (2016) 12. G.E. Jellison Jr., L.A. Boatner, J.D. Budai, J. Appl. Phys. 93, 9537 (2003) 13. G.E. Jellison Jr., F.A. Modine, L.A. Boatner, Opt. Lett. 22, 1808 (1997) 14. T. Hara, T. Maekawa, S. Minoura, Y. Sago, S. Niki, H. Fujiwara, Phys. Rev. Appl. 2, 034012 (2014)

Chapter 12

Metals Shohei Fujimoto, Takemasa Fujiseki and Hiroyuki Fujiwara

Abstract The dielectric functions and optical constants of various metals, which have been incorporated into solar cell devices as front and rear electrodes, are summarized. The metals described here include the group-Ib (Cu, Ag, Au), IIa (Mg), IIIb (Al), IVa (Ti), VIa (Cr, Mo, W), and VIII (Ni, Pt) metals. The optical constants of C (graphite), which has been applied widely for CdTe solar cells, are also shown. It is established in this chapter that the metal dielectric functions in the whole near-infrared/visible/ultraviolet region (1–5 eV) can be parameterized almost perfectly by the combined use of the Tauc-Lorentz and Drude models. For the modeling with the Tauc-Lorentz model, several transition peaks are assumed in the analyzed region. In this chapter, the parameterization results for all the metals are summarized, together with the tabulated optical constants. The dielectric function and optical constants of various metals are also compared. Moreover, the reflectances at semiconductor/metal interfaces in crystalline Si, Cu(In,Ga)Se2 and hybrid perovskite [HC(NH2)2PbI3] solar cells are calculated and their results are discussed.

12.1

Introduction

Metal electrodes are a vital component in photovoltaic devices, serving also as optical back reflector in the case of rear electrodes. In solar cells, the reduction of the short-circuit current density (Jsc) occurs by the parasitic optical absorption in metal back electrodes, and the optical loss increases rather significantly when the reflectance at absorber/metal interfaces is low. Since the back-side reflection is determined essentially by the optical properties of the rear metal contact, the optical constants of rear metals are of particular concern for the optimization of device structures. In Cu(In,Ga)Se2 (CIGSe) and Cu2ZnSn(S,Se)4 (CZTSSe) solar cells, for example, Mo layers formed on soda-lime glass substrates show weak reflectance (Sect. 12.2) and the necessity of using Mo rear electrodes in these solar cells leads S. Fujimoto ⋅ T. Fujiseki ⋅ H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_12

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to the Jsc loss of ∼3 mA/cm2 (Sect. 2.6). In optical simulations, if a metal layer is sufficiently thick (typically >10 nm), this layer should be treated as a substrate material, as there is negligible light transmission though the metal layer. In this chapter, for the purpose of spectroscopic ellipsometry (SE) characterization and device simulation, the tabulated optical constants of various metals at room temperature are provided. In addition, the optical properties of C graphite, which can also be employed as a rear electrode, are described here. For all the metals and semimetal, refractive index n and extinction coefficient k are shown in a wavelength (λ) range of 300–1200 nm with steps of 5 nm (300–400 nm) and 10 nm (400– 1200 nm). From these numerical values, the dielectric function (ε = ε1 – iε2) and the absorption coefficient (α) can be calculated quite easily according to ε1 = n2 − k2, ε2 = 2nk and α = 4πk/λ (Sect. 1.2.1). The λ value can also be converted to energy (E) by E = 1239.8/[λ (nm)] eV (1.3). Unfortunately, the tabulated data are sometimes insufficient for more complete SE analysis or optical simulation. Accordingly, all the dielectric functions of the metals and semimetal were parameterized by combining the Tauc-Lorentz model with the Drude model (see Sect. 1.2.3). The Tauc-Lorentz model was developed originally to express the dielectric function of amorphous materials [1], but we found that the combination of the Tauc-Lorentz model with the Drude model is quite effective for the complete parameterization of metal dielectric functions. However, it should be emphasized that the Tauc-Lorentz model is used solely to establish the optical database of various solar-cell component layers. By combining several Tauc-Lorentz peaks with a single Drude term, the dielectric functions of various metals are reproduced almost perfectly in a wide photon energy range (E = 1−5 eV) using an unified parameterization scheme. In the actual modeling, the dielectric functions of the metals and semimetal were calculated using (11.1) and (11.2). The calculation example of the Tauc-Lorentz model is also shown in (1.26). A free software described in Sect. 2.7 can further be applied to calculate the dielectric function from the Tauc-Lorentz and Drude parameters listed in this chapter. In this chapter, in addition to the optical data of metals, the basic optical properties of metals are explained. Moreover, for crystal Si (c-Si), CIGSe and hybrid perovskite solar cells, the reflectances at semiconductor/metal interfaces are calculated for different metal materials. Based on the results obtained from the calculations, we further discuss the parasitic light absorption in metal electrodes.

12.2

Optical Properties and Reflectance of Metals

In this section, the optical constants of metals are compared to understand the optical properties of metals. The various reflectance spectra calculated for different semiconductor/metal interfaces are also presented.

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12.2.1 Optical Properties of Metals Figure 12.1 shows the dielectric functions (ε1, ε2) and the optical constants (n, k) of selected metals versus photon energy. The optical data of each material can be found in Sect. 12.3. As confirmed from the figure, all the metals show negative ε1 values at low energies, whereas many metals exhibit very large ε2 values in the lowE region. The decrease in ε1 and the increase in ε2 with reducing energy are the specific feature of the free carrier absorption (see Fig. 1.9c), which is induced by the light absorption of free electrons (Chap. 18 in Vol. 1). The free carrier absorption can be expressed rather simply using the Drude model described by (1.27). In metals, however, the optical transitions from the d bands also occur [2] and each metal shows different features. The negative ε1 values observed in metal materials can be related to the reflectance at metal interfaces. In particular, when a metal has a large negative value, the propagation of an electromagnetic wave into the metal is hindered strongly and the reflectance at the metal interface increases. For example, Ag and Al exhibit large negative ε1 values in a wide region in Fig. 12.1. In this case, all

Fig. 12.1 Dielectric functions (ε1, ε2) and optical constants (n, k) of selected metals (Ag, Al, Au, Mo, Ni, and Pt) versus photon energy. The optical data described in this chapter are summarized. Note that the ε1 values of Al are reduced to half for clarity

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Fig. 12.2 Dielectric functions (ε1, ε2) and optical constants (n, k) of selected metals versus wavelength. The optical data described in this chapter are summarized. Note that the ε1 values of Al are reduced to half for clarity

near-infrared, visible and ultraviolet light is reflected strongly, resulting in a whitish color on Ag and Al metal surfaces. In contrast, ε1 of Au shows a drop in the visible region (E < 2.5 eV) and the reflectance for the green/blue light is weaker. This is the reason why the color of Au looks yellowish (or reddish). In (n, k) spectra, on the other hand, n shows a positive value and the (n, k) values increase at lower energies due to the effect of free carrier absorption. Notice that the overall k values of the metals are quite large, indicating strong light absorption in the materials. Figure 12.2 shows the same optical data as in Fig. 12.1, but the optical spectra are shown versus λ. From the above spectra, the reflectance spectra at semiconductor/ metal interfaces can be calculated.

12.2.2 Reflectance at Semiconductor/Metal Interface The reflectance R at material interfaces can be calculated rather easily by applying the Fresnel equations assuming the normal incidence [i.e., θi = 0° in (3.15) in Vol. 1]:

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NM − Ni 2 2 R = rp = jrs j2 = NM + Ni

ð12:1Þ

where rp and rs show the amplitude reflection coefficients for p- and s-polarizations. In the above equation, NM and Ni represent the complex refractive indices (N ≡ n − ik) of a metal and an incident medium (i.e., air, semiconductor, etc.). By inserting NM = nM − ikM and Ni = ni − iki into (12.1), we obtain (nM − ni ) − iðkM − ki Þ 2 (nM − ni )2 + ðkM − ki Þ2 = R = (nM + ni ) − iðkM + ki Þ (nM + ni )2 + ðkM + ki Þ2

ð12:2Þ

Thus, R simply increases if the differences in n and k at the interface become larger. Figure 12.3 shows the R spectra calculated for air/metal, c-Si/metal, CuIn0.6Ga0.4Se2/metal and hybrid perovskite/metal interfaces using different metal materials (i.e., Al, Ag, Au, Pt, Ni and Mo). For Ni, we employed Ni = ni = 1 (air) and the optical data shown in Fig. 8.1(c-Si), Fig. 8.26 (CuIn0.6Ga0.4Se2) and Fig. 10.1 [α-FAPbI3, HC(NH2)2PbI3], whereas the optical functions in Fig. 12.2 were applied for NM. Note that, in CIGSe solar cells prepared by conventional three-stage coevaporation, the Ga composition is modified continuously toward the growth direction and the double-grading Ga profile is formed. The Ga composition of CuIn1–xGaxSe2 at the rear interface is typically x ∼ 0.4 (see Fig. 2.8). Thus, the calculation result for CuIn0.6Ga0.4Se2 is shown in Fig. 12.3. It can be confirmed that Al, Ag and Au show high R values in a wide spectral region, compared with the other metals. Since R increases when the “optical contrast” between the two interface materials is larger, the R values obtained for the air/metal interfaces are higher than those for the semiconductor/metal interfaces. Figure 12.4 compares the R spectra for the rear interfaces in actual solar cells. For c-Si solar cells, Al and Ag rear electrodes are generally employed (Sect. 2.5.2), whereas Au and Ag metals are used for hybrid perovskite solar cells (Sect. 16.3 in Vol. 1). In solar cells, external quantum efficiency (EQE) response in a longer λ region is quite important and high R near the band gap (Eg) is crucial to suppress the parasitic absorption in rear metal electrodes (Chap. 2). In the c-Si and hybrid perovskite solar cells, R near Eg (1100 nm in c-Si and 800 nm in α-FAPbI3) is sufficiently high. In contrast, at the CuIn0.6Ga0.4Se2/Mo interface, R is only 36% near Eg (1100 nm) and the EQE response in the longer λ region reduces by the light absorption in the Mo layer (Fig. 2.11). The lower R at the CIGSe/Mo interface is caused by the optical properties of Mo. Specifically, Mo shows ε1 ∼ 0 in a broad region of E > 1.5 eV (see Fig. 12.1). Since R increases when ε1 shows a large negative value, Mo is not a good reflector. As a result, Cu-Se containing solar cells (i.e., CIGSe and CZTSSe solar cells), which use Mo rear electrodes, suffer from relatively large parasitic absorption in Mo (Table 2.1).

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Fig. 12.3 R spectra calculated for air/metal, c-Si/metal, CuIn0.6Ga0.4Se2/metal and hybrid perovskite/metal interfaces using different metal materials (Al, Ag, Au, Pt, Ni and Mo)

Fig. 12.4 R spectra calculated for c-Si/Al, CuIn0.6Ga0.4Se2/Mo and αFAPbI3/Au interfaces formed in actual solar cells. The results are consistent with those shown in Fig. 12.3

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As confirmed from (12.2), the contribution of R at the interface can be separated into two factors concerning n and k: R = Rn + Rk .

ð12:3Þ

Here, Rn and Rk show the R factors induced by the difference in n and k, respectively. If A = (nM + ni)2 + (kM + ki)2 is applied for (12.2), Rn and Rk are expressed by Rn = (nM − ni )2 ̸A, Rk = ðkM − ki Þ2 ̸ A.

ð12:4Þ

Figure 12.5 summarizes Rn and Rk spectra calculated for (a) the CuIn0.6Ga0.4Se2/ metal and (b) the α-FAPbI3/metal interfaces. If we focus on R in the Eg region, R is determined predominantly by Rk and the contribution of Rn is low (Rn < 15%). To achieve high R at the rear interface, therefore, high-k metals are important. Unfortunately, for Cu-Se containing solar cells, the current fabrication processes favor the use of Mo layers. Accordingly, to enhance R at the rear interface of these solar cells, Mo alloys including Mo-Al, Mo-Ag and Mo-Au could be applied.

Fig. 12.5 Rn and Rk spectra calculated for a the CuIn0.6Ga0.4Se2/metal and b the α-FAPbI3/metal interfaces using (12.4)

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Optical Data of Metals

12.3.1 Ag Data: unpublished results of Gifu University. The optical data have been extracted from a dc sputtered Ag layer (Fig. 12.6, Tables 12.1 and 12.2).

Fig. 12.6 Dielectric function of Ag at room temperature. The open circles show the experimental data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.1 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Ag Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 TL peak6 Drude

3.671 1.305 0.162 233.000 85.379 23.454 74.909

2.344 1.904 0.700 0.572 1.825 1.256 0.039

1.179 2.381 3.339 3.949 4.130 5.322 –

0.427 0.863 0.217 3.748 3.766 4.840 –

1.928 0 0 0 0 0 –

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Table 12.2 Optical constants of Ag calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.508 1.499 1.432 1.280 1.027 0.667 0.320 0.234 0.207 0.195 0.190 0.189 0.188 0.187 0.186 0.183 0.180 0.175 0.170 0.165 0.160 0.152 0.147 0.143 0.141 0.140 0.139 0.139 0.138 0.138 0.138 0.138 0.137 0.137

1.008 0.867 0.694 0.516 0.376 0.343 0.579 0.843 1.022 1.159 1.272 1.369 1.454 1.530 1.599 1.663 1.724 1.783 1.841 1.898 1.954 2.063 2.169 2.270 2.369 2.464 2.556 2.647 2.735 2.822 2.907 2.991 3.074 3.156

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

0.137 0.136 0.136 0.136 0.135 0.135 0.134 0.134 0.134 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.134 0.134 0.135 0.135 0.136 0.136 0.137 0.138 0.138 0.139 0.140 0.141 0.142 0.143 0.144 0.145 0.146 0.147

3.237 3.317 3.397 3.477 3.556 3.634 3.712 3.790 3.868 3.945 4.022 4.099 4.175 4.252 4.328 4.404 4.479 4.555 4.630 4.705 4.780 4.855 4.929 5.004 5.078 5.152 5.226 5.300 5.374 5.447 5.521 5.594 5.668 5.741

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

0.148 0.150 0.151 0.152 0.153 0.155 0.156 0.157 0.159 0.160 0.162 0.163 0.165 0.166 0.168 0.169 0.171 0.173 0.174 0.176 0.178 0.180 0.181 0.183 0.185 0.187 0.189 0.191 0.193 0.195 0.197 0.199 0.201

5.814 5.887 5.960 6.033 6.106 6.178 6.251 6.324 6.396 6.469 6.541 6.613 6.685 6.758 6.830 6.902 6.974 7.046 7.118 7.190 7.262 7.334 7.405 7.477 7.549 7.620 7.692 7.764 7.835 7.907 7.978 8.050 8.121

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12.3.2 Al Data from S. Adachi [3] (Fig. 12.7, Tables 12.3 and 12.4).

Fig. 12.7 Dielectric function of Al at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.3 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Al Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 Drude

369.196 5.604 15.459 179.505

0.269 0.335 1.214 0.121

1.341 1.578 1.616 –

1.280 1 × 10−4 1 × 10−4 –

0.885 0 0 –

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Table 12.4 Optical constants of Al calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

0.279 0.287 0.296 0.305 0.314 0.324 0.333 0.342 0.352 0.362 0.372 0.382 0.393 0.404 0.414 0.425 0.437 0.448 0.459 0.471 0.483 0.508 0.533 0.560 0.587 0.616 0.645 0.676 0.707 0.740 0.774 0.809 0.846 0.883

3.614 3.678 3.741 3.804 3.867 3.930 3.993 4.055 4.118 4.181 4.243 4.306 4.368 4.430 4.493 4.555 4.617 4.679 4.741 4.803 4.865 4.988 5.111 5.234 5.357 5.479 5.601 5.723 5.844 5.965 6.085 6.205 6.324 6.443

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

0.923 0.963 1.006 1.049 1.095 1.142 1.191 1.241 1.294 1.350 1.408 1.469 1.534 1.603 1.677 1.757 1.844 1.937 2.039 2.147 2.262 2.380 2.494 2.599 2.686 2.749 2.784 2.791 2.773 2.734 2.678 2.608 2.525 2.430

6.561 6.678 6.795 6.911 7.026 7.140 7.253 7.365 7.477 7.587 7.696 7.804 7.911 8.015 8.118 8.217 8.311 8.399 8.477 8.544 8.595 8.625 8.632 8.615 8.576 8.521 8.456 8.391 8.331 8.281 8.242 8.215 8.199 8.195

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.323 2.204 2.076 1.943 1.813 1.694 1.592 1.511 1.452 1.414 1.385 1.360 1.338 1.319 1.301 1.285 1.271 1.259 1.248 1.238 1.229 1.222 1.215 1.210 1.205 1.202 1.199 1.197 1.195 1.195 1.194 1.195 1.196

8.205 8.232 8.280 8.353 8.451 8.574 8.716 8.870 9.029 9.183 9.326 9.462 9.595 9.726 9.854 9.981 10.106 10.231 10.354 10.477 10.599 10.721 10.841 10.962 11.082 11.201 11.320 11.439 11.557 11.675 11.792 11.910 12.027

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12.3.3 Au To express the dielectric function of Au, two separate data sets are used depending on the energy region: (i) S. Adachi [3] for E ≥ 1.6 eV and (ii) E. D. Palik [4] for E ≤ 1.5 eV (Fig. 12.8, Tables 12.5 and 12.6).

Fig. 12.8 Dielectric function of Au at room temperature. The plots show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.5 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Au Model TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 Drude

A/AD (eV) 4.485 31.570 104.771 150.616 12.628 82.101

C/Γ (eV) 0.933 1.884 0.997 6.282 1.566 0.040

E0 (eV) 0.774 2.444 2.574 3.489 4.077 –

ε1(∞)

Eg (eV) −4

1 × 10 1.669 2.267 3.414 1.468 –

2.710 0 0 0 0 –

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Table 12.6 Optical constants of Au calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.790 1.818 1.840 1.853 1.859 1.858 1.851 1.839 1.824 1.807 1.790 1.773 1.757 1.744 1.734 1.724 1.717 1.710 1.705 1.700 1.696 1.687 1.673 1.650 1.612 1.553 1.468 1.353 1.210 1.045 0.876 0.719 0.590 0.492

1.936 1.922 1.903 1.883 1.863 1.845 1.830 1.819 1.812 1.809 1.812 1.818 1.827 1.838 1.850 1.862 1.873 1.884 1.893 1.900 1.906 1.909 1.902 1.884 1.855 1.819 1.783 1.756 1.750 1.779 1.851 1.963 2.104 2.258

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

0.421 0.373 0.335 0.302 0.274 0.249 0.229 0.211 0.197 0.185 0.175 0.167 0.160 0.156 0.153 0.151 0.150 0.150 0.151 0.153 0.155 0.158 0.162 0.165 0.168 0.172 0.175 0.179 0.182 0.186 0.190 0.194 0.198 0.202

2.413 2.561 2.697 2.827 2.953 3.075 3.195 3.312 3.427 3.540 3.651 3.759 3.866 3.971 4.075 4.177 4.277 4.375 4.473 4.569 4.663 4.756 4.848 4.938 5.028 5.116 5.204 5.292 5.378 5.464 5.550 5.634 5.719 5.803

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

0.206 0.210 0.214 0.218 0.222 0.227 0.231 0.235 0.240 0.244 0.248 0.253 0.257 0.262 0.266 0.271 0.276 0.280 0.285 0.289 0.294 0.299 0.303 0.308 0.313 0.317 0.322 0.327 0.331 0.336 0.341 0.345 0.350

5.886 5.969 6.052 6.134 6.216 6.297 6.379 6.460 6.540 6.620 6.700 6.780 6.860 6.939 7.018 7.097 7.176 7.254 7.332 7.410 7.488 7.565 7.643 7.720 7.797 7.874 7.951 8.027 8.104 8.180 8.256 8.332 8.408

556

S. Fujimoto et al.

12.3.4 C (Graphite) Data from S. Adachi [3]. Graphite single crystals exhibit uniaxial optical anisotropy with the optical axis perpendicular to the basal (graphite C) plane. Here, the optical data for the ordinary ray (ε⊥: the electric field parallel to the basal plane) are summarized (Fig. 12.9, Tables 12.7 and 12.8).

Fig. 12.9 Dielectric function of C (graphite). The ε⊥ represents the dielectric function parallel to the basal plane (ordinary ray). The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.7 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for ε⊥ of C (graphite) Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 TL peak6 Drude

10.191 44.915 38.793 9.322 21.746 7.683 3.058

0.091 1.535 0.049 2.208 2.053 0.941 0.222

0.830 0.959 1.155 2.216 3.449 4.460 –

0.311 0.416 1.133 0.127 1.532 1 × 10−4 –

3.544 0 0 0 0 0 –

12

Metals

557

Table 12.8 Optical constants for the ordinary ray in C (graphite) calculated by the Tauc-Lorentz and Drude models (N⊥ = n⊥ − ik⊥) λ (nm)

n⊥

k⊥

λ (nm)

n⊥

k⊥

λ (nm)

n⊥

k⊥

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.792 2.787 2.771 2.752 2.732 2.715 2.701 2.690 2.682 2.677 2.674 2.673 2.672 2.673 2.673 2.674 2.674 2.674 2.673 2.672 2.670 2.665 2.658 2.650 2.643 2.637 2.632 2.629 2.629 2.630 2.634 2.640 2.648 2.658

1.768 1.674 1.601 1.545 1.504 1.473 1.450 1.432 1.419 1.407 1.398 1.389 1.381 1.373 1.365 1.357 1.350 1.343 1.337 1.331 1.327 1.320 1.317 1.318 1.324 1.333 1.346 1.361 1.378 1.397 1.417 1.437 1.458 1.478

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.669 2.682 2.695 2.710 2.724 2.740 2.755 2.771 2.787 2.803 2.818 2.834 2.849 2.864 2.878 2.893 2.907 2.921 2.935 2.949 2.962 2.975 2.988 3.001 3.014 3.026 3.039 3.051 3.063 3.075 3.087 3.099 3.110 3.121

1.498 1.517 1.536 1.553 1.570 1.586 1.602 1.616 1.630 1.644 1.656 1.669 1.681 1.692 1.703 1.714 1.725 1.736 1.746 1.757 1.767 1.777 1.787 1.797 1.807 1.817 1.827 1.837 1.847 1.856 1.866 1.875 1.884 1.894

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.132 3.143 3.153 3.164 3.174 3.183 3.193 3.202 3.211 3.220 3.228 3.237 3.245 3.254 3.264 3.275 3.289 3.305 3.323 3.327 3.306 3.280 3.266 3.257 3.249 3.241 3.233 3.225 3.216 3.206 3.196 3.185 3.174

1.903 1.912 1.921 1.930 1.940 1.949 1.958 1.968 1.977 1.987 1.997 2.008 2.018 2.029 2.040 2.051 2.060 2.066 2.061 2.042 2.029 2.040 2.061 2.081 2.101 2.121 2.143 2.166 2.190 2.216 2.245 2.276 2.309

558

S. Fujimoto et al.

12.3.5 Cr Data from S. Adachi [3] (Fig. 12.10, Tables 12.9 and 12.10).

Fig. 12.10 Dielectric function of Cr at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.9 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Cr Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 TL peak6 Drude

40.348 22.164 18.218 6.058 34.747 18.194 33.203

1.727 1.221 1.320 0.907 0.789 6.730 0.295

1.325 1.618 2.147 2.445 3.365 8.473 –

1 × 10−4 0.456 0.492 8 × 10−4 2.713 0.623 –

1.137 0 0 0 0 0 –

12

Metals

559

Table 12.10 Optical constants of Cr calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

0.982 1.007 1.034 1.064 1.096 1.130 1.166 1.205 1.243 1.282 1.319 1.352 1.380 1.402 1.418 1.430 1.439 1.448 1.460 1.475 1.495 1.550 1.624 1.715 1.820 1.938 2.066 2.200 2.338 2.475 2.606 2.730 2.844 2.946

2.663 2.724 2.784 2.843 2.900 2.954 3.006 3.054 3.098 3.138 3.173 3.204 3.233 3.261 3.291 3.326 3.367 3.414 3.468 3.526 3.587 3.714 3.841 3.962 4.075 4.176 4.264 4.336 4.391 4.429 4.451 4.459 4.457 4.447

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.036 3.117 3.189 3.255 3.314 3.370 3.422 3.471 3.518 3.563 3.606 3.648 3.690 3.730 3.770 3.809 3.847 3.885 3.923 3.959 3.995 4.029 4.063 4.096 4.127 4.157 4.186 4.214 4.240 4.265 4.289 4.311 4.332 4.351

4.434 4.419 4.405 4.392 4.381 4.372 4.365 4.359 4.355 4.353 4.351 4.351 4.351 4.352 4.353 4.354 4.355 4.356 4.357 4.357 4.357 4.356 4.355 4.353 4.350 4.347 4.344 4.340 4.336 4.332 4.328 4.324 4.319 4.315

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

4.370 4.387 4.402 4.417 4.431 4.443 4.455 4.466 4.475 4.484 4.492 4.499 4.505 4.510 4.515 4.519 4.522 4.524 4.526 4.527 4.528 4.528 4.527 4.526 4.524 4.522 4.519 4.515 4.511 4.507 4.502 4.497 4.491

4.311 4.307 4.304 4.300 4.297 4.294 4.292 4.290 4.289 4.287 4.287 4.286 4.287 4.287 4.288 4.290 4.292 4.294 4.297 4.300 4.304 4.308 4.313 4.319 4.324 4.331 4.338 4.345 4.353 4.361 4.370 4.380 4.390

560

S. Fujimoto et al.

12.3.6 Cu To express the dielectric function of Cu, two separate data sets are used depending on the energy region: (i) A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski [5] for E ≥ 1 eV, (ii) E. D. Palik [4] for 0.616 ≤ E < 1 eV (Fig. 12.11, Tables 12.11 and 12.12).

Fig. 12.11 Dielectric function of Cu at room temperature. The plots show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.11 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Cu Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 TL peak6 Drude

4.912 32.533 19.338 97.523 24.330 54.887 74.866

0.472 0.289 0.477 1.112 1.922 1.980 0.052

0.744 0.998 2.234 2.257 3.514 4.789 –

0.060 0.987 1.694 1.952 2.182 3.317 –

1.968 0 0 0 0 0 –

12

Metals

561

Table 12.12 Optical constants of Cu calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.364 1.346 1.331 1.319 1.309 1.301 1.295 1.289 1.284 1.279 1.273 1.267 1.260 1.253 1.246 1.238 1.230 1.222 1.214 1.206 1.198 1.184 1.172 1.163 1.155 1.150 1.145 1.140 1.134 1.127 1.118 1.106 1.088 1.060

1.712 1.732 1.756 1.780 1.805 1.829 1.853 1.876 1.899 1.920 1.942 1.963 1.984 2.005 2.027 2.049 2.072 2.095 2.119 2.143 2.168 2.219 2.271 2.322 2.372 2.419 2.463 2.504 2.540 2.573 2.600 2.622 2.635 2.638

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.014 0.941 0.840 0.718 0.593 0.481 0.390 0.323 0.277 0.247 0.231 0.221 0.215 0.212 0.210 0.211 0.212 0.214 0.218 0.221 0.225 0.229 0.233 0.238 0.242 0.247 0.251 0.256 0.261 0.265 0.270 0.275 0.280 0.285

2.633 2.629 2.639 2.679 2.755 2.864 2.993 3.132 3.272 3.408 3.537 3.657 3.771 3.881 3.986 4.088 4.187 4.284 4.378 4.470 4.560 4.649 4.736 4.822 4.908 4.992 5.075 5.158 5.240 5.321 5.401 5.481 5.561 5.640

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

0.290 0.295 0.301 0.306 0.311 0.316 0.321 0.326 0.332 0.337 0.342 0.347 0.352 0.357 0.361 0.366 0.371 0.375 0.379 0.383 0.387 0.391 0.394 0.397 0.400 0.403 0.406 0.408 0.411 0.414 0.417 0.420 0.424

5.719 5.797 5.874 5.952 6.029 6.105 6.181 6.257 6.332 6.408 6.482 6.557 6.631 6.705 6.779 6.853 6.926 6.999 7.072 7.145 7.218 7.291 7.363 7.436 7.509 7.583 7.656 7.730 7.804 7.879 7.954 8.030 8.106

562

S. Fujimoto et al.

12.3.7 Mg To express the dielectric function of Mg, three separate data sets are used: (i) S. Adachi [3], (ii) E. D. Palik [6], and (iii) R. Machorro, J. M. Siqueiros, and S. Wang [7] (Fig. 12.12, Tables 12.13 and 12.14).

Fig. 12.12 Dielectric function of Mg at room temperature. The plots show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.13 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Mg Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 Drude

83.530 6.007 28.474 86.155

0.164 0.282 0.253 0.190

0.781 1.048 1.538 –

0.185 1 × 10−4 1.357 –

1.545 0 0 –

12

Metals

563

Table 12.14 Optical constants of Mg calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

0.099 0.102 0.105 0.108 0.111 0.114 0.117 0.120 0.124 0.127 0.130 0.134 0.137 0.141 0.144 0.148 0.151 0.155 0.159 0.163 0.167 0.175 0.183 0.191 0.200 0.209 0.218 0.227 0.237 0.247 0.257 0.268 0.278 0.290

2.534 2.587 2.640 2.692 2.744 2.796 2.848 2.900 2.952 3.004 3.055 3.107 3.158 3.209 3.261 3.312 3.363 3.414 3.465 3.516 3.567 3.669 3.771 3.872 3.974 4.075 4.177 4.278 4.380 4.482 4.583 4.685 4.787 4.889

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

0.301 0.313 0.325 0.338 0.351 0.364 0.378 0.392 0.407 0.423 0.439 0.456 0.473 0.491 0.510 0.530 0.551 0.572 0.595 0.618 0.642 0.666 0.689 0.710 0.728 0.741 0.749 0.753 0.755 0.759 0.766 0.777 0.793 0.812

4.991 5.094 5.196 5.299 5.402 5.505 5.608 5.712 5.815 5.919 6.024 6.128 6.232 6.337 6.442 6.546 6.650 6.754 6.857 6.959 7.060 7.159 7.256 7.350 7.443 7.536 7.632 7.733 7.840 7.954 8.074 8.197 8.322 8.448

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

0.835 0.861 0.890 0.921 0.953 0.988 1.024 1.063 1.103 1.146 1.190 1.238 1.288 1.340 1.396 1.455 1.516 1.581 1.650 1.721 1.795 1.872 1.951 2.031 2.113 2.194 2.275 2.354 2.431 2.505 2.575 2.642 2.705

8.575 8.702 8.829 8.956 9.083 9.210 9.337 9.465 9.593 9.722 9.851 9.980 10.110 10.240 10.370 10.499 10.628 10.755 10.882 11.007 11.129 11.249 11.366 11.480 11.590 11.696 11.799 11.899 11.997 12.093 12.189 12.286 12.386

564

S. Fujimoto et al.

12.3.8 Mo Data from T. Hara, T. Maekawa, S. Minoura, Y. Sago, S. Niki and H. Fujiwara [8]. The optical data have been extracted from a Mo layer formed by sputtering (Fig. 12.13, Tables 12.15 and 12.16).

Fig. 12.13 Dielectric function of Mo at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.15 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Mo Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 Drude

34.298 42.314 86.182 196.919 27.947

1.871 1.005 1.520 2.390 0.168

0.961 1.616 2.144 2.642 –

0.021 0.851 1.562 2.639 –

1.261 0 0 0 –

12

Metals

565

Table 12.16 Optical constants of Mo. The optical data reported by Hara et al. are shown λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.601 1.628 1.655 1.680 1.704 1.727 1.750 1.771 1.790 1.809 1.826 1.843 1.858 1.871 1.884 1.896 1.906 1.916 1.925 1.933 1.941 1.955 1.969 1.985 2.005 2.029 2.060 2.099 2.146 2.194 2.241 2.286 2.328 2.367

2.281 2.295 2.308 2.320 2.332 2.343 2.353 2.363 2.372 2.381 2.390 2.399 2.408 2.417 2.427 2.437 2.448 2.459 2.472 2.485 2.499 2.531 2.568 2.610 2.656 2.706 2.757 2.807 2.849 2.883 2.912 2.935 2.955 2.972

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.404 2.437 2.468 2.496 2.521 2.545 2.567 2.588 2.609 2.630 2.651 2.672 2.693 2.715 2.737 2.759 2.781 2.802 2.822 2.841 2.857 2.872 2.884 2.894 2.902 2.907 2.910 2.910 2.908 2.902 2.893 2.882 2.868 2.852

2.986 2.999 3.011 3.023 3.036 3.048 3.062 3.076 3.092 3.107 3.123 3.139 3.155 3.169 3.183 3.195 3.205 3.213 3.220 3.225 3.228 3.230 3.231 3.231 3.230 3.230 3.229 3.228 3.227 3.226 3.227 3.230 3.235 3.241

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.835 2.817 2.797 2.777 2.756 2.735 2.714 2.693 2.673 2.653 2.634 2.616 2.598 2.581 2.565 2.550 2.537 2.524 2.512 2.501 2.491 2.481 2.473 2.466 2.459 2.453 2.448 2.443 2.439 2.436 2.434 2.432 2.430

3.250 3.262 3.276 3.292 3.310 3.331 3.354 3.380 3.407 3.436 3.466 3.498 3.532 3.567 3.603 3.640 3.677 3.716 3.755 3.795 3.835 3.876 3.917 3.958 4.000 4.041 4.083 4.125 4.167 4.208 4.250 4.292 4.333

566

S. Fujimoto et al.

12.3.9 Ni Data from S. Adachi [3] (Fig. 12.14, Tables 12.17 and 12.18).

Fig. 12.14 Dielectric function of Ni at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.17 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Ni Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 Drude

4.525 17.513 22.171 49.193 50.010

0.600 1.366 3.617 2.198 0.398

1.058 1.565 3.221 4.429 –

1 × 10−4 0.027 0.352 2.701 –

2.082 0 0 0 –

12

Metals

567

Table 12.18 Optical constants of Ni calculated by the Tauc-Lorentz and Drude models λ (nm) 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

n 1.737 1.733 1.725 1.715 1.703 1.690 1.677 1.664 1.653 1.642 1.633 1.625 1.618 1.612 1.608 1.605 1.603 1.601 1.601 1.601 1.602 1.605 1.610 1.616 1.623 1.631 1.641 1.651 1.662 1.674 1.686 1.699 1.714 1.729

k 1.999 1.990 1.986 1.986 1.990 1.998 2.011 2.026 2.045 2.065 2.088 2.113 2.138 2.165 2.193 2.221 2.249 2.277 2.306 2.335 2.364 2.422 2.480 2.538 2.596 2.654 2.713 2.771 2.829 2.888 2.947 3.006 3.066 3.127

λ (nm) 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

n 1.746 1.765 1.785 1.806 1.829 1.854 1.880 1.907 1.935 1.965 1.995 2.026 2.058 2.090 2.123 2.156 2.189 2.221 2.253 2.285 2.316 2.346 2.375 2.404 2.431 2.457 2.482 2.506 2.529 2.550 2.571 2.590 2.608 2.626

k 3.187 3.247 3.307 3.367 3.426 3.485 3.543 3.599 3.655 3.709 3.761 3.812 3.862 3.910 3.956 4.000 4.043 4.084 4.123 4.161 4.197 4.232 4.266 4.299 4.331 4.361 4.391 4.421 4.450 4.479 4.508 4.536 4.565 4.594

λ (nm) 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

n 2.642 2.658 2.673 2.688 2.702 2.715 2.729 2.742 2.755 2.768 2.780 2.793 2.806 2.819 2.832 2.845 2.858 2.871 2.884 2.897 2.909 2.922 2.934 2.946 2.957 2.968 2.979 2.988 2.998 3.006 3.014 3.021 3.028

k 4.623 4.652 4.681 4.711 4.742 4.772 4.803 4.835 4.866 4.898 4.931 4.963 4.995 5.028 5.060 5.093 5.125 5.157 5.189 5.220 5.252 5.282 5.313 5.343 5.373 5.402 5.432 5.461 5.490 5.519 5.547 5.576 5.605

568

12.3.10

S. Fujimoto et al.

Pt

Data from S. Adachi [3] (Fig. 12.15, Tables 12.19 and 12.20).

Fig. 12.15 Dielectric function of Pt at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.19 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Pt Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 Drude

93.659 76.972 29.551 49.047

1.362 3.016 16.080 0.464

0.880 1.601 8.477 –

0.216 1.011 1 × 10−4 –

2.282 0 0 –

12

Metals

569

Table 12.20 Optical constants of Pt calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.462 1.472 1.483 1.494 1.505 1.516 1.528 1.539 1.551 1.563 1.575 1.587 1.600 1.612 1.625 1.638 1.651 1.664 1.677 1.690 1.703 1.730 1.757 1.784 1.812 1.840 1.868 1.896 1.924 1.952 1.980 2.008 2.036 2.064

2.174 2.209 2.243 2.278 2.312 2.346 2.380 2.414 2.448 2.482 2.515 2.548 2.581 2.614 2.647 2.679 2.712 2.744 2.776 2.807 2.839 2.901 2.963 3.024 3.084 3.144 3.203 3.261 3.319 3.376 3.432 3.488 3.543 3.598

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.093 2.121 2.149 2.177 2.205 2.233 2.261 2.290 2.318 2.346 2.374 2.402 2.431 2.459 2.487 2.516 2.545 2.573 2.602 2.631 2.660 2.689 2.718 2.748 2.777 2.807 2.837 2.867 2.897 2.927 2.957 2.988 3.018 3.049

3.653 3.707 3.760 3.813 3.866 3.918 3.970 4.022 4.073 4.124 4.175 4.226 4.276 4.326 4.375 4.424 4.474 4.522 4.571 4.619 4.667 4.715 4.762 4.809 4.856 4.903 4.949 4.995 5.040 5.086 5.130 5.175 5.219 5.263

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.080 3.111 3.142 3.173 3.204 3.236 3.267 3.299 3.330 3.362 3.394 3.425 3.457 3.489 3.521 3.553 3.584 3.616 3.648 3.680 3.712 3.744 3.775 3.807 3.839 3.870 3.902 3.933 3.965 3.996 4.027 4.058 4.090

5.307 5.350 5.393 5.435 5.477 5.519 5.560 5.601 5.641 5.681 5.721 5.760 5.799 5.837 5.875 5.913 5.950 5.987 6.023 6.059 6.095 6.130 6.165 6.199 6.233 6.267 6.300 6.333 6.365 6.397 6.429 6.460 6.491

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Ti

Data from E. D. Palik [6] (Fig. 12.16, Tables 12.21 and 12.22).

Fig. 12.16 Dielectric function of Ti at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.21 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for Ti Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 TL peak6 Drude

51.696 18.731 4.457 5.288 21.875 167.447 9.997

1.560 0.670 0.941 1.563 1.031 3.032 0.172

0.924 1.460 1.987 2.965 3.296 3.899 –

0.127 0.816 0.934 1 × 10−4 2.616 3.878 –

1.343 0 0 0 0 0 –

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Table 12.22 Optical constants of Ti calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.045 1.038 1.040 1.051 1.071 1.099 1.131 1.165 1.200 1.237 1.274 1.310 1.345 1.378 1.408 1.436 1.462 1.485 1.506 1.526 1.545 1.579 1.612 1.642 1.669 1.693 1.714 1.733 1.751 1.768 1.784 1.802 1.820 1.841

1.500 1.559 1.621 1.684 1.745 1.800 1.849 1.893 1.932 1.966 1.995 2.020 2.041 2.059 2.074 2.087 2.099 2.111 2.122 2.134 2.145 2.170 2.194 2.217 2.241 2.264 2.289 2.316 2.346 2.377 2.411 2.448 2.486 2.526

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.863 1.888 1.914 1.943 1.974 2.005 2.038 2.072 2.106 2.141 2.177 2.212 2.249 2.287 2.325 2.365 2.406 2.448 2.492 2.537 2.584 2.631 2.679 2.727 2.774 2.822 2.868 2.912 2.955 2.995 3.032 3.067 3.099 3.128

2.568 2.609 2.651 2.692 2.732 2.771 2.809 2.845 2.881 2.916 2.950 2.983 3.016 3.049 3.080 3.111 3.141 3.170 3.197 3.222 3.245 3.265 3.283 3.298 3.309 3.318 3.323 3.326 3.326 3.323 3.319 3.313 3.306 3.298

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.153 3.176 3.197 3.215 3.231 3.245 3.258 3.270 3.281 3.291 3.301 3.310 3.320 3.329 3.339 3.349 3.359 3.370 3.381 3.392 3.404 3.416 3.429 3.441 3.455 3.468 3.482 3.496 3.510 3.524 3.539 3.554 3.568

3.290 3.283 3.276 3.270 3.265 3.261 3.259 3.258 3.259 3.261 3.264 3.269 3.275 3.282 3.290 3.298 3.307 3.317 3.328 3.338 3.349 3.360 3.372 3.383 3.395 3.406 3.418 3.429 3.440 3.451 3.462 3.472 3.483

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W

Data from S. Adachi [3] (Fig. 12.17, Table 12.23 and 12.24).

Fig. 12.17 Dielectric function of W at room temperature. The open circles show the reference data and the lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz (solid lines) and Drude (dotted line) models [(11.1) and (11.2)]

Table 12.23 Tauc-Lorentz (TL) peak and Drude parameters of (11.1) and (11.2) for W Model

A/AD (eV)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 TL peak4 TL peak5 TL peak6 TL peak7 TL peak8 Drude

11.433 70.027 74.001 15.009 54.766 19.398 27.618 67.404 37.346

0.585 0.381 1.900 0.468 0.527 1.947 0.495 2.014 0.098

1.000 1.680 1.755 2.372 3.343 3.418 5.236 5.270 –

1 × 10−4 1.524 0.665 1.889 2.838 0.447 3.910 1.802 –

2.240 0 0 0 0 0 0 0 –

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Table 12.24 Optical constants of W calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.987 2.968 2.958 2.957 2.965 2.982 3.008 3.043 3.086 3.138 3.196 3.260 3.323 3.380 3.422 3.446 3.450 3.441 3.424 3.405 3.386 3.355 3.332 3.317 3.309 3.307 3.311 3.321 3.338 3.364 3.395 3.429 3.458 3.478

2.359 2.389 2.425 2.464 2.505 2.546 2.586 2.622 2.654 2.679 2.694 2.696 2.682 2.650 2.605 2.554 2.505 2.467 2.439 2.423 2.415 2.416 2.432 2.455 2.484 2.517 2.552 2.590 2.628 2.663 2.690 2.708 2.716 2.720

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

3.489 3.495 3.500 3.507 3.518 3.534 3.554 3.577 3.603 3.631 3.661 3.693 3.725 3.757 3.787 3.814 3.835 3.847 3.849 3.839 3.816 3.783 3.742 3.697 3.651 3.607 3.565 3.527 3.494 3.462 3.431 3.400 3.369 3.339

2.725 2.736 2.753 2.776 2.801 2.827 2.852 2.875 2.896 2.913 2.926 2.934 2.937 2.934 2.924 2.906 2.881 2.850 2.815 2.779 2.747 2.720 2.703 2.697 2.699 2.710 2.728 2.750 2.774 2.798 2.823 2.849 2.876 2.906

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.308 3.278 3.249 3.221 3.194 3.168 3.143 3.120 3.099 3.080 3.063 3.048 3.036 3.026 3.018 3.012 3.008 3.007 3.007 3.010 3.014 3.020 3.027 3.035 3.044 3.054 3.064 3.074 3.084 3.094 3.103 3.112 3.119

2.937 2.971 3.007 3.044 3.084 3.125 3.169 3.213 3.260 3.307 3.356 3.406 3.456 3.506 3.556 3.606 3.656 3.705 3.753 3.799 3.845 3.888 3.930 3.970 4.009 4.045 4.079 4.110 4.140 4.167 4.192 4.215 4.237

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References 1. G.E. Jellison, Jr., F.A. Modine. Appl. Phys. Lett. 69, 371 (1996); Erratum. Appl. Phys. Lett. 69, 2137 (1996) 2. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, West Sussex, UK, 2007) 3. S. Adachi, The Handbook on Optical Constants of Metals: in Tables and Figures (World Scientific, Singapore, 2012) 4. E.D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985) 5. A.D. Rakic, A.B. Djurisic, J.M. Elazar, M.L. Majewski. Appl. Opt. 37, 5271 (1998) 6. E.D. Palik, Handbook of Optical Constants of Solids III (Academic, San Diego, 1998) 7. R. Machorro, J.M. Siqueiros, S. Wang, Thin solid films 269, 1 (1995) 8. T. Hara, T. Maekawa, S. Minoura, Y. Sago, S. Niki, H. Fujiwara, Phys. Rev. Appl. 2, 034012 (2014)

Chapter 13

Substrates and Coating Layers Shohei Fujimoto, Takemasa Fujiseki, James N. Hilfiker, Nina Hong, Mariano Campoy-Quiles and Hiroyuki Fujiwara

Abstract The optical constants of various substrates and coating materials employed widely for solar-cell fabrication are summarized. The substrate materials described here include various SiO2 (soda-lime glass, borosilicate glass, fused silica, and quartz), metal (stainless) and plastic (polycarbonate, PEN, PET, PMMA, Kapton HN) substrates. For PEN, PET and Kapton HN substrates, which exhibit strong biaxial optical anisotropy, full data sets are provided. In solar cell devices, a protection coating (EVA) and anti-reflection (MgF2/LiF) layers are quite important, and the optical constants of these coating layers are also described here. The refractive index spectra of the transparent materials were parameterized using the Sellmeier model, whereas the parameterization of absorbing polymer substrates was carried out assuming several transition peaks calculated by the Tauc-Lorentz model. In this chapter, the model parameters for all the substrates and coating materials are summarized, together with the tabulated optical constants.

13.1

Introduction

For the preparation of solar cells, various substrates made of glass, metal and polymer have been used. In particular, for light-weight flexible solar cells, thin stainless steel and polymer substrates have been applied. The optical properties of

S. Fujimoto ⋅ T. Fujiseki ⋅ H. Fujiwara (✉) Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan e-mail: [email protected] J. N. Hilfiker ⋅ N. Hong J.A. Woollam Co., Inc., 645 M Street, Suite 102, Lincoln, NE 68508, USA M. Campoy-Quiles Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, 08193 Bellaterra, Spain © Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6_13

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solar-cell substrates are quite important particularly for superstrate-type solar cells in which sunlight passes through the thick substrates. To reduce the front light reflection of solar cells, on the other hand, MgF2 and LiF anti-reflection layers are employed widely. Moreover, in crystalline-Si modules, an organic protection layer (EVA) is generally formed on the solar-cell front surface. For spectroscopic ellipsometry (SE) characterization and optical simulation of solar cell devices, it is necessary to have all the optical constants of the solar-cell component layers. In this chapter, therefore, the tabulated optical constants of various substrates and anti-reflection/protection layers at room temperature are provided. In particular, for most materials, refractive index n and extinction coefficient k are shown in a wavelength (λ) range of 300–1200 nm with steps of 5 nm (300–400 nm) and 10 nm (400–1200 nm). From these numerical values, the dielectric function (ε = ε1 − iε2) and the absorption coefficient (α) can be calculated quite easily according to ε1 = n2 − k2, ε2 = 2nk and α = 4πk/λ (Sect. 1.2.1). The λ value can also be converted to energy (E) by E = 1239.8/[λ (nm)] eV (1.3). It should be noted that, in the tabulated data, the absolute k value is denoted as “0” when there is no observable light absorption, even though materials may have very small k (or α) value in a certain E region. For some substrates (soda-lime glass, polycarbonate, PMMA, Kapton HN) and EVA, however, the k values in a range of 10−5 ∼ 10−4 are shown, as rather strong light absorption still occurs in these materials even with the small k values due to large thicknesses of the substrate (∼5 mm) and the EVA film (∼100 μm). Unfortunately, the tabulated data are sometimes insufficient for more complete SE analysis or optical simulation. Accordingly, all the optical constants of substrates and coating layers were parameterized assuming (i) the Sellmeier model or (ii) the Tauc-Lorentz model (see Fig. 1.9). Specifically, for optically transparent materials, the following Sellmeier model was used. n2 ðλÞ =

B1 λ2 B λ2 B λ2
+ 2 2
+ 2 3
+1 λ − C1 λ − C2 λ − C3 2

ð13:1Þ

In this model, there are a total of six parameters (B1, B2, B3, C1, C2, C3) and the n spectrum can be calculated quite easily from these parameter values while assuming k = 0. On the other hand, the Tauc-Lorentz model (Sect. 1.2.3) is quite effective for the parameterization of organic materials (Chap. 9) and metals (Chap. 12). In particular, by combining several Tauc-Lorentz peaks, the dielectric functions of isotropic/ anisotropic plastic substrates can be expressed, although the Tauc-Lorentz model is used solely to establish the optical database for various solar-cell component materials. When only limited spectral information is available, however, the

13

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577

Tauc-Lorentz model is also applied to extrapolate the spectrum beyond experimental data to cover the consistent spectral range of 300–1200 nm. In the actual modeling of plastic substrates (polycarbonate, PEN, PET and Kapton HN), the dielectric functions were calculated using (8.1) and (8.2), while the dielectric function of a stainless substrate was modeled by further incorporating the Drude term [see (11.1) and (11.2)]. The calculation example of the Tauc-Lorentz model is shown in (1.26). A free software described in Sect. 2.7 can further be applied to calculate the dielectric function from the model parameters listed in this chapter. All the parameterizations of the optical constants described in this chapter were implemented by the group of Gifu University (S. Fujimoto and T. Fujiseki), unless otherwise noted.

13.2

Optical Data of Substrates and Coating Layers

13.2.1 SiO2 The refractive index spectra of various SiO2 substrates reported in the following references are summarized: (i) (ii) (iii) (iv) (v)

Soda-lime glass: R. A. Synowicki, B. D. Johs, and A. C. Martin [1], Eagle XG glass: unpublished results of Gifu university, Borosilicate (BK7) glass: SCHOTT optical glass data sheets [2], Fused silica: I. H. Malitson [3], Quartz: G. Gosh [4].

The refractive index spectra of soda-lime, Eagle XG and quartz substrates are parameterized using the Sellmeier model of (13.1). For borosilicate and fused silica substrates, however, the Sellmeier parameters are taken from the above references. In general, soda-lime glass substrates are produced by floating molten SiO2 on liquid Sn. As a result, the Sn-side and air-side of the soda-lime glass show slightly different optical properties. Here, the optical constants that correspond to the bulk component of a soda-lime glass substrate are indicated. On the other hand, quartz substrates exhibit small optical anisotropy and the optical data for ordinary and extraordinary rays are summarized (Fig. 13.1, Tables 13.1, 13.2, 13.3, 13.4, 13.5, 13.6 and 13.7).

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Fig. 13.1 Optical constants of SiO2 at room temperature. The refractive index spectra (solid lines) represent the calculation results obtained from the Sellmeier model expressed by (13.1) and the extinction-coefficient spectrum for the soda-lime glass (open circles) shows the experimental data reported by Synowicki et al. [1]

Table 13.1 Sellmeier parameters of (13.1) for various SiO2 substrates. The reported parameter values are adopted for the substrates of borosilicate glass [2] and fused silica [3] Material

B1

B2

C1 (μm2)

B3

−3

C2 (μm2)

C3 (μm2) –

Soda-lime glass

1.263

0.334

–

9.90 × 10

43.346

Eagle XG glass

1.132

0.120

8.85 × 10−2

6.81 × 10−3

2.48 × 10−2

10.105

Borosilicate glass

1.040

0.232

1.010

6.00 × 10−3

2.00 × 10−2

103.561

Fused silica

0.696

0.408

0.897

4.68 × 10−3

1.35 × 10−2

Quartz (ordinary)

1.353

0.212

–

8.41 × 10−3

24.647

–

Quartz (extraordinary)

1.380

0.223

–

8.57 × 10−3

24.647

–

97.935

Table 13.2 Optical constants of soda-lime glass. The optical data of the bulk component reported by Synowicki et al. are shown λ (nm) 305 310 315 320 325 330 335 340

n 1.5514 1.5504 1.5490 1.5478 1.5465 1.5451 1.5438 1.5426

k ( × 10−5) 5.1791 4.0846 3.0913 2.1865 1.4904 0.9815 0.6739 0.4446

λ (nm) 550 560 570 580 590 600 610 620

n 1.5177 1.5172 1.5167 1.5162 1.5157 1.5152 1.5148 1.5143

k ( × 10−5) 0.0196 0.0196 0.0221 0.0270 0.0319 0.0370 0.0393 0.0467

λ (nm) 890 900 910 920 930 940 950 960

n 1.5072 1.5071 1.5069 1.5067 1.5066 1.5063 1.5061 1.5060

k ( × 10−5) 0.2955 0.3076 0.3189 0.3313 0.3414 0.3534 0.3632 0.3753 (continued)

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Table 13.2 (continued) 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540

1.5415 1.5404 1.5393 1.5381 1.5373 1.5364 1.5356 1.5348 1.5340 1.5331 1.5323 1.5315 1.5301 1.5287 1.5275 1.5264 1.5254 1.5245 1.5235 1.5226 1.5218 1.5211 1.5203 1.5196 1.5190 1.5184

0.3106 0.2206 0.1518 0.1104 0.0859 0.0652 0.0517 0.0466 0.0442 0.0417 0.0392 0.0344 0.0294 0.0270 0.0245 0.0222 0.0221 0.0245 0.0245 0.0245 0.0221 0.0220 0.0196 0.0172 0.0172 0.0196

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880

1.5138 1.5134 1.5131 1.5127 1.5123 1.5119 1.5116 1.5113 1.5110 1.5108 1.5105 1.5102 1.5099 1.5097 1.5095 1.5093 1.5091 1.5089 1.5087 1.5085 1.5083 1.5081 1.5079 1.5078 1.5076 1.5074

0.0564 0.0662 0.0737 0.0809 0.0883 0.0982 0.1055 0.1154 0.1251 0.1374 0.1445 0.1546 0.1619 0.1693 0.1767 0.1839 0.1939 0.2012 0.2087 0.2208 0.2307 0.2405 0.2501 0.2625 0.2724 0.2849

970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.5058 1.5057 1.5055 1.5054 1.5052 1.5051 1.5050 1.5048 1.5047 1.5045 1.5044 1.5043 1.5043 1.5041 1.5040 1.5040 1.5039 1.5038 1.5037 1.5037 1.5036 1.5035 1.5034 1.5034

0.3853 0.3951 0.4042 0.4120 0.4221 0.4294 0.4368 0.4417 0.4466 0.4515 0.4564 0.4589 0.4589 0.4613 0.4613 0.4613 0.4613 0.4613 0.4590 0.4589 0.4564 0.4540 0.4515 0.4491

Table 13.3 Refractive index of Eagle XG glass calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

300 305 310 315 320 325 330 335 340 345 350

1.5458 1.5441 1.5425 1.5409 1.5395 1.5381 1.5369 1.5356 1.5345 1.5334 1.5323

460 470 480 490 500 510 520 530 540 550 560

1.5178 1.5170 1.5162 1.5155 1.5148 1.5142 1.5136 1.5130 1.5125 1.5120 1.5115

720 730 740 750 760 770 780 790 800 810 820

1.5061 1.5058 1.5056 1.5054 1.5052 1.5050 1.5047 1.5045 1.5043 1.5041 1.5040

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080

n 1.5013 1.5012 1.5010 1.5009 1.5007 1.5006 1.5005 1.5003 1.5002 1.5000 1.4999 (continued)

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S. Fujimoto et al.

Table 13.3 (continued) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.5313 1.5304 1.5295 1.5286 1.5278 1.5270 1.5262 1.5255 1.5248 1.5241 1.5228 1.5217 1.5206 1.5196 1.5187

570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.5110 1.5106 1.5102 1.5098 1.5094 1.5090 1.5087 1.5084 1.5080 1.5077 1.5074 1.5071 1.5069 1.5066 1.5063

830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.5038 1.5036 1.5034 1.5032 1.5031 1.5029 1.5027 1.5026 1.5024 1.5022 1.5021 1.5019 1.5018 1.5016 1.5015

1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4998 1.4996 1.4995 1.4994 1.4992 1.4991 1.4989 1.4988 1.4987 1.4985 1.4984 1.4983

Table 13.4 Refractive index of borosilicate glass calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395

1.5530 1.5512 1.5496 1.5481 1.5466 1.5452 1.5439 1.5427 1.5415 1.5404 1.5394 1.5384 1.5374 1.5365 1.5356 1.5347 1.5339 1.5332 1.5324 1.5317

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650

1.5246 1.5238 1.5230 1.5223 1.5216 1.5210 1.5204 1.5198 1.5192 1.5187 1.5182 1.5178 1.5173 1.5169 1.5165 1.5161 1.5157 1.5154 1.5150 1.5147

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910

1.5127 1.5125 1.5123 1.5120 1.5118 1.5116 1.5114 1.5112 1.5110 1.5108 1.5106 1.5104 1.5102 1.5100 1.5099 1.5097 1.5095 1.5094 1.5092 1.5090

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170

n 1.5080 1.5078 1.5077 1.5076 1.5074 1.5073 1.5072 1.5070 1.5069 1.5068 1.5066 1.5065 1.5064 1.5062 1.5061 1.5060 1.5059 1.5057 1.5056 1.5055 (continued)

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Substrates and Coating Layers

581

Table 13.4 (continued) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

400 410 420 430 440 450

1.5310 1.5298 1.5286 1.5275 1.5265 1.5255

660 670 680 690 700 710

1.5144 1.5141 1.5138 1.5135 1.5133 1.5130

920 930 940 950 960 970

1.5089 1.5087 1.5086 1.5084 1.5083 1.5081

1180 1190 1200

1.5054 1.5052 1.5051

Table 13.5 Refractive index of fused silica calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.4877 1.4864 1.4851 1.4838 1.4827 1.4816 1.4805 1.4795 1.4786 1.4777 1.4768 1.4760 1.4752 1.4745 1.4738 1.4731 1.4724 1.4718 1.4712 1.4706 1.4701 1.4690 1.4680 1.4671 1.4663 1.4655

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.4648 1.4641 1.4635 1.4629 1.4623 1.4617 1.4612 1.4608 1.4603 1.4599 1.4595 1.4591 1.4587 1.4583 1.4580 1.4577 1.4574 1.4571 1.4568 1.4565 1.4562 1.4560 1.4557 1.4555 1.4553 1.4550

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.4548 1.4546 1.4544 1.4542 1.4540 1.4538 1.4536 1.4535 1.4533 1.4531 1.4529 1.4528 1.4526 1.4525 1.4523 1.4522 1.4520 1.4519 1.4517 1.4516 1.4514 1.4513 1.4512 1.4510 1.4509 1.4508

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4506 1.4505 1.4504 1.4503 1.4501 1.4500 1.4499 1.4498 1.4496 1.4495 1.4494 1.4493 1.4492 1.4490 1.4489 1.4488 1.4487 1.4486 1.4485 1.4484 1.4482 1.4481 1.4480

582

S. Fujimoto et al.

Table 13.6 Refractive index of quartz (ordinary) calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.5785 1.5769 1.5754 1.5740 1.5726 1.5713 1.5701 1.5690 1.5679 1.5668 1.5658 1.5648 1.5639 1.5630 1.5622 1.5614 1.5606 1.5598 1.5591 1.5584 1.5578 1.5565 1.5554 1.5543 1.5533 1.5524

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.5515 1.5507 1.5499 1.5492 1.5485 1.5479 1.5473 1.5467 1.5462 1.5457 1.5452 1.5447 1.5443 1.5438 1.5434 1.5431 1.5427 1.5423 1.5420 1.5417 1.5414 1.5411 1.5408 1.5405 1.5402 1.5400

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.5397 1.5395 1.5392 1.5390 1.5388 1.5386 1.5384 1.5382 1.5380 1.5378 1.5376 1.5374 1.5372 1.5371 1.5369 1.5367 1.5365 1.5364 1.5362 1.5361 1.5359 1.5358 1.5356 1.5355 1.5353 1.5352

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.5350 1.5349 1.5348 1.5346 1.5345 1.5344 1.5342 1.5341 1.5340 1.5338 1.5337 1.5336 1.5335 1.5333 1.5332 1.5331 1.5330 1.5329 1.5327 1.5326 1.5325 1.5324 1.5323

Table 13.7 Refractive index of quartz (extraordinary) calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

300 305 310 315 320 325 330 335 340 345 350

1.5888 1.5872 1.5856 1.5842 1.5828 1.5814 1.5802 1.5789 1.5778 1.5767 1.5757

460 470 480 490 500 510 520 530 540 550 560

1.5609 1.5600 1.5592 1.5585 1.5578 1.5571 1.5565 1.5559 1.5554 1.5548 1.5543

720 730 740 750 760 770 780 790 800 810 820

1.5487 1.5484 1.5482 1.5479 1.5477 1.5475 1.5473 1.5471 1.5469 1.5467 1.5465

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080

n 1.5438 1.5437 1.5435 1.5434 1.5433 1.5431 1.5430 1.5428 1.5427 1.5426 1.5424 (continued)

13

Substrates and Coating Layers

583

Table 13.7 (continued) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.5747 1.5737 1.5728 1.5719 1.5711 1.5703 1.5695 1.5688 1.5681 1.5674 1.5661 1.5649 1.5638 1.5627 1.5618

570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.5538 1.5534 1.5529 1.5525 1.5521 1.5518 1.5514 1.5510 1.5507 1.5504 1.5501 1.5498 1.5495 1.5492 1.5489

830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.5463 1.5461 1.5459 1.5457 1.5456 1.5454 1.5452 1.5450 1.5449 1.5447 1.5446 1.5444 1.5443 1.5441 1.5440

1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.5423 1.5422 1.5421 1.5419 1.5418 1.5417 1.5415 1.5414 1.5413 1.5412 1.5410 1.5409

13.2.2 Stainless Steel (SUS304) Data: unpublished results of T. Fujiseki. The optical data have been extracted from a mirror-polished stainless substrate (SUS304). No particular surface treatment of the sample was made before the ellipsometry measurement (Fig. 13.2, Tables 13.8 and 13.9).

Fig. 13.2 Dielectric function of stainless steel at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz and Drude models expressed by (11.1) and (11.2)

584

S. Fujimoto et al.

Table 13.8 Tauc-Lorentz and Drude parameters for stainless steel Model

A/AD (ΓL)

C/Γ (eV)

E0 (eV)

Eg (eV)

ε1(∞)

TL peak1 TL peak2 TL peak3 Drude

132.086 172.262 29.284 80.655

0.392 1.967 5.569 1.114

0.660 1.068 5.695 –

0.656 0.805 1.935 –

1.816 0 0 –

Table 13.9 Optical constants of stainless steel calculated by the Tauc-Lorentz and Drude models λ (nm)

n

k

λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.323 1.329 1.336 1.344 1.353 1.362 1.372 1.383 1.395 1.407 1.420 1.433 1.448 1.463 1.478 1.494 1.511 1.528 1.545 1.563 1.581 1.619 1.659 1.699 1.741 1.784 1.827 1.871 1.916 1.961 2.007 2.053 2.099 2.145

2.265 2.302 2.340 2.378 2.416 2.455 2.494 2.533 2.572 2.612 2.651 2.690 2.729 2.767 2.806 2.844 2.882 2.919 2.957 2.994 3.030 3.102 3.173 3.242 3.309 3.375 3.439 3.502 3.563 3.622 3.680 3.736 3.791 3.844

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.192 2.238 2.284 2.331 2.377 2.423 2.469 2.514 2.559 2.604 2.649 2.693 2.737 2.780 2.823 2.866 2.907 2.949 2.989 3.029 3.069 3.108 3.146 3.184 3.221 3.257 3.293 3.328 3.363 3.397 3.431 3.464 3.496 3.528

3.896 3.946 3.995 4.043 4.089 4.134 4.178 4.221 4.263 4.303 4.343 4.381 4.418 4.454 4.490 4.524 4.558 4.590 4.622 4.653 4.684 4.714 4.743 4.772 4.800 4.828 4.855 4.882 4.908 4.934 4.959 4.985 5.009 5.034

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

3.559 3.590 3.620 3.650 3.679 3.708 3.736 3.764 3.791 3.818 3.844 3.870 3.896 3.921 3.946 3.971 3.995 4.019 4.042 4.065 4.088 4.111 4.133 4.156 4.177 4.199 4.221 4.242 4.263 4.284 4.305 4.326 4.346

5.059 5.083 5.107 5.130 5.154 5.178 5.201 5.224 5.247 5.270 5.293 5.316 5.339 5.362 5.385 5.408 5.431 5.454 5.477 5.500 5.523 5.546 5.569 5.592 5.616 5.639 5.662 5.685 5.709 5.732 5.755 5.779 5.802

13

Substrates and Coating Layers

585

13.2.3 Polycarbonate Data: unpublished results of J. N. Hilfiker. The optical data of a 3-mm-thick polycarbonate substrate have been extracted by analyzing three SE spectra measured at three different incident angles (55°, 65°, 75°) and a transmittance spectrum simultaneously (Fig. 13.3, Tables 13.10 and 13.11).

Fig. 13.3 Optical constants of polycarbonate at room temperature. The open circles show the experimental data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 13.10 Tauc-Lorentz parameters of (8.1) and (8.2) for polycarbonate Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

4.01 × 10−5 3.03 × 10−4 3.022 170.307 14.504 26.397 12.430 885.063

0.513 0.490 0.150 0.333 0.528 0.419 0.409 2.927

2.108 3.693 4.606 5.378 5.771 6.053 6.280 9.052

1.252 1.717 3.935 4.791 3.099 3.499 3.500 7.963

0.828 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

586

S. Fujimoto et al.

Table 13.11 Optical constants of polycarbonate calculated by the Tauc-Lorentz model λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

2.896 2.870 2.846 2.824 2.805 2.786 2.770 2.755 2.740 2.727 2.715 2.704 2.693 2.683 2.674 2.665 2.657 2.649 2.642 2.635 2.628 2.616 2.605 2.595 2.586 2.578 2.570 2.564 2.557 2.551 2.546 2.541 2.536 2.532

1.15 9.34 7.56 6.10 4.90 3.90 3.08 2.40 1.86 1.42 1.08 8.26 6.27 4.63 3.29 2.22 1.39 7.79 3.61 1.20 3.78 3.00 2.46 2.09 1.84 1.66 1.55 1.50 1.49 1.52 1.58 1.69 1.83 2.00

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−5 10−5 10−5 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6

λ (nm)

n

k

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

2.527 2.524 2.520 2.517 2.513 2.510 2.507 2.505 2.502 2.500 2.497 2.495 2.493 2.491 2.489 2.488 2.486 2.484 2.483 2.481 2.48 2.479 2.477 2.476 2.475 2.474 2.473 2.472 2.471 2.470 2.469 2.468 2.467 2.466

2.19 2.38 2.55 2.67 2.71 2.64 2.48 2.25 1.98 1.72 1.46 1.24 1.04 8.78 7.39 6.23 5.26 4.45 3.78 3.22 2.74 2.34 2.00 1.70 1.44 1.23 1.05 0 0 0 0 0 0 0

× × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7 10−7

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

2.465 2.465 2.464 2.463 2.462 2.462 2.461 2.460 2.460 2.459 2.459 2.458 2.458 2.457 2.457 2.456 2.456 2.455 2.455 2.454 2.454 2.453 2.453 2.453 2.452 2.452 2.451 2.451 2.451 2.450 2.450 2.450 2.450

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

13

Substrates and Coating Layers

587

13.2.4 PEN [Poly(Ethylene Naphthalate)] Data from N. Hong, R. A. Synowicki, and J. N. Hilfiker [5]. The biaxial optical anisotropy of a PEN substrate (DuPont Teijin Films) has been characterized by Mueller-matrix SE in reflection and transmission modes. Full SE data sets obtained at different incident and sample rotation angles were analyzed to extract the optical data. The biaxial material has different optical constants for polarizations along the x, y, and z axes: i.e., Nx = nx − ikx, Ny = ny − iky, and Nz = nz − ikz. For the z direction, however, only the non-absorbing region has been characterized assuming kz = 0. In the case of a PEN substrate, the light absorption in the substrate can be estimated as an average of kx and ky, as the electric fields of incident light can be decomposed into the components parallel to the x and y axes (see also Fig. 13.4b) (Tables 13.12, 13.13, 13.14, 13.15, 13.16 and 13.17).

Fig. 13.4 a Chemical structure, b coordinate system, and c room-temperature optical constants of PEN. For the light polarization along the x, y, and z axes in b, the optical constants are defined by Nx = nx − ikx, Ny = ny − iky and Nz = nz − ikz. For the k spectra, only the in-plane components are shown. In c, the open circles show the experimental data and the solid lines indicate the calculation results obtained from the parameterization assuming the Tauc-Lorentz model expressed by (8.1) and (8.2). For the refractive index spectrum of nz, however, the Sellmeier model expressed by (13.1) was applied

588

S. Fujimoto et al.

Table 13.12 Tauc-Lorentz parameters of (8.1) and (8.2) for εx = (Nx)2 of PEN Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

4.630 0.468 1.446 4.053 3.593 97.800 4.202 205.741

8.58 × 10−2 0.132 0.136 0.249 0.889 0.375 0.954 2.240

3.467 3.635 4.116 4.266 4.504 4.868 5.317 6.301

3.169 2.742 3.269 3.497 3.404 4.533 2.831 6.301

1.741 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 13.13 Tauc-Lorentz parameters of (8.1) and (8.2) for εy = (Ny)2 of PEN Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j j

6.379 10.167 0.734 14.971 5.572 49.304 8.273 2.092 71.440

6.58 × 10−2 0.132 0.116 0.248 0.711 0.304 0.475 0.764 1.278

3.477 3.605 4.116 4.257 4.569 4.921 5.193 5.646 7.060

3.284 3.423 2.414 3.634 3.320 4.214 3.323 2.658 6.084

1.936 0 0 0 0 0 0 0 0

= = = = = = = = =

1 2 3 4 5 6 7 8 9

Table 13.14 Sellmeier parameters of (13.1) for nz of PEN Material

B1

B2

B3

C1 (μm2)

C2 (μm2)

C3 (μm2)

PEN

1.202

0.207

–

1.28 × 10−2

604.127

–

Table 13.15 Optical constants of Nx = nx − ikx for PEN reported by Hong et al. λ (nm)

nx

kx

λ (nm)

nx

kx

300 305 310 315 320 325 330 335 340

1.932 1.976 1.932 1.898 1.865 1.832 1.817 1.788 1.802

0.202 0.121 6.54 × 4.41 × 2.99 × 3.20 × 3.90 × 4.74 × 8.09 ×

540 550 560 570 580 590 600 610 620

1.705 1.703 1.701 1.699 1.698 1.696 1.695 1.694 1.692

1.08 × 10−4 1.04 × 10−4 1.01 × 10−4 9.8 × 10−5 9.5 × 10−5 9.2 × 10−5 9.0 × 10−5 8.8 × 10−5 8.6 × 10−5

10−2 10−2 10−2 10−2 10−2 10−2 10−2

λ (nm) 880 890 900 910 920 930 940 950 960

nx

kx

1.675 1.675 1.674 1.674 1.674 1.673 1.673 1.673 1.672

5.4 × 10−5 5.4 × 10−5 5.3 × 10−5 5.2 × 10−5 5.1 × 10−5 5.1 × 10−5 5.0 × 10−5 5.0 × 10−5 4.9 × 10−5 (continued)

13

Substrates and Coating Layers

589

Table 13.15 (continued) λ (nm)

nx

kx

345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.809 1.800 1.794 1.872 1.853 1.827 1.810 1.797 1.787 1.779 1.773 1.767 1.758 1.750 1.743 1.737 1.732 1.728 1.724 1.720 1.717 1.714 1.712 1.709 1.707

6.78 5.58 0.11 8.02 2.16 7.68 2.66 1.06 6.97 5.82 5.07 4.47 3.55 2.90 2.45 2.12 1.87 1.69 1.55 1.44 1.35 1.28 1.21 1.16 1.12

× 10−2 × 10−2 × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4

λ (nm)

nx

kx

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.691 1.690 1.689 1.688 1.687 1.686 1.685 1.685 1.684 1.683 1.683 1.682 1.681 1.681 1.680 1.680 1.679 1.678 1.678 1.678 1.677 1.677 1.676 1.676 1.675

8.4 8.2 8.0 7.8 7.7 7.5 7.4 7.2 7.1 7.0 6.8 6.7 6.6 6.5 6.4 6.3 6.2 6.1 6.0 5.9 5.8 5.7 5.7 5.6 5.5

× × × × × × × × × × × × × × × × × × × × × × × × ×

10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5

λ (nm)

nx

kx

970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.672 1.672 1.672 1.671 1.671 1.671 1.671 1.670 1.670 1.670 1.670 1.670 1.669 1.669 1.669 1.669 1.669 1.668 1.668 1.668 1.668 1.668 1.667 1.667

4.8 4.8 4.7 4.7 4.6 4.6 4.5 4.5 4.4 4.4 4.3 4.3 4.2 4.2 4.1 4.1 4.1 4.0 4.0 3.9 3.9 3.9 3.8 3.8

× × × × × × × × × × × × × × × × × × × × × × × ×

10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5

Table 13.16 Optical constants of Ny = ny − iky for PEN reported by Hong et al. λ (nm)

ny

ky

λ (nm)

ny

ky

300 305 310 315 320 325 330 335 340

2.203 2.308 2.215 2.154 2.098 2.044 2.029 1.984 1.991

0.381 0.21 0.105 6.61 × 4.10 × 4.17 × 4.78 × 4.86 × 6.40 ×

540 550 560 570 580 590 600 610 620

1.794 1.791 1.789 1.786 1.784 1.782 1.780 1.778 1.776

2.11 2.03 1.95 1.87 1.80 1.74 1.68 1.63 1.58

10−2 10−2 10−2 10−2 10−2 10−2

λ (nm) × × × × × × × × ×

10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4

880 890 900 910 920 930 940 950 960

ny

ky

1.751 1.750 1.750 1.749 1.749 1.749 1.748 1.748 1.747

8.8 × 10−5 8.7 × 10−5 8.6 × 10−5 8.4 × 10−5 8.3 × 10−5 8.2 × 10−5 8.1 × 10−5 7.9 × 10−5 7.8 × 10−5 (continued)

590

S. Fujimoto et al.

Table 13.16 (continued) λ (nm)

ny

ky

345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.995 1.976 1.971 2.013 1.965 1.943 1.928 1.916 1.906 1.897 1.889 1.882 1.870 1.859 1.850 1.841 1.834 1.828 1.822 1.817 1.812 1.808 1.804 1.800 1.797

6.53 3.39 7.92 3.40 1.85 1.47 1.21 1.02 8.74 7.66 6.82 6.17 5.23 4.60 4.14 3.78 3.49 3.25 3.04 2.86 2.70 2.56 2.43 2.31 2.21

× × × × × × × × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4

λ (nm)

ny

ky

λ (nm)

ny

ky

630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.774 1.773 1.771 1.770 1.768 1.767 1.766 1.765 1.764 1.763 1.762 1.761 1.760 1.759 1.758 1.757 1.757 1.756 1.755 1.755 1.754 1.753 1.753 1.752 1.752

1.53 × 10−4 1.48 × 10−4 1.44 × 10−4 1.40 × 10−4 1.36 × 10−4 1.33 × 10−4 1.29 × 10−4 1.26 × 10−4 1.23 × 10−4 1.20 × 10−4 1.18 × 10−4 1.15 × 10−4 1.13 × 10−4 1.10 × 10−4 1.08 × 10−4 1.06 × 10−4 1.04 × 10−4 1.02 × 10−4 1.00 × 10−4 9.8 × 10−5 9.6 × 10−5 9.5 × 10−5 9.3 × 10−5 9.1 × 10−5 9.0 × 10−5

970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.747 1.746 1.746 1.746 1.745 1.745 1.745 1.744 1.744 1.744 1.743 1.743 1.743 1.743 1.742 1.742 1.742 1.741 1.741 1.741 1.741 1.740 1.740 1.740

7.7 7.6 7.5 7.4 7.3 7.2 7.1 7.0 7.0 6.9 6.8 6.7 6.6 6.6 6.5 6.4 6.3 6.3 6.2 6.1 6.1 6.0 5.9 5.9

× × × × × × × × × × × × × × × × × × × × × × × ×

10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5

Table 13.17 Refractive index of nz for PEN reported by Hong et al. (k = 0) λ (nm)

nz

λ (nm)

nz

380 385 390 395 400 410 420 430 440 450

1.5223 1.5213 1.5202 1.5193 1.5183 1.5166 1.5149 1.5134 1.5120 1.5107

580 590 600 610 620 630 640 650 660 670

1.4996 1.4990 1.4985 1.4980 1.4975 1.4971 1.4967 1.4962 1.4959 1.4955

λ (nm) 800 810 820 830 840 850 860 870 880 890

nz

λ (nm)

1.4918 1.4916 1.4914 1.4912 1.4911 1.4909 1.4907 1.4905 1.4904 1.4902

1020 1030 1040 1050 1060 1070 1080 1090 1100 1110

nz 1.4886 1.4885 1.4884 1.4883 1.4882 1.4881 1.4880 1.4879 1.4879 1.4878 (continued)

13

Substrates and Coating Layers

591

Table 13.17 (continued) λ (nm)

nz

λ (nm)

nz

λ (nm)

nz

λ (nm)

nz

460 470 480 490 500 510 520 530 540 550 560 570

1.5095 1.5084 1.5073 1.5063 1.5054 1.5045 1.5037 1.5029 1.5022 1.5015 1.5008 1.5002

680 690 700 710 720 730 740 750 760 770 780 790

1.4951 1.4948 1.4945 1.4941 1.4938 1.4936 1.4933 1.4930 1.4928 1.4925 1.4923 1.4921

900 910 920 930 940 950 960 970 980 990 1000 1010

1.4901 1.4899 1.4898 1.4896 1.4895 1.4894 1.4893 1.4891 1.4890 1.4889 1.4888 1.4887

1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4877 1.4876 1.4876 1.4875 1.4874 1.4874 1.4873 1.4872 1.4872

13.2.5 PET [Poly(Ethylene Terephthalate)] Data from N. Hong, R. A. Synowicki, and J. N. Hilfiker [5]. The biaxial optical anisotropy of a 50-μm-thick PET substrate (DuPont Teijin Films) has been characterized by Mueller-matrix SE in reflection and transmission modes. Full SE data sets obtained at different incident and sample rotation angles were analyzed to extract the optical data. The biaxial material has different optical constants for polarizations along the x, y, and z axes: i.e., Nx = nx − ikx, Ny = ny − iky, and Nz = nz − ikz. For the z direction, however, only the non-absorbing region has been characterized assuming kz = 0. In the case of a PET substrate, the light absorption in the substrate can be estimated as an average of kx and ky, as the electric fields of incident light can be decomposed into the components parallel to the x and y axes (see also Fig. 13.5b) (Tables 13.18, 13.19, 13.20, 13.21, 13.22 and 13.23).

592

S. Fujimoto et al.

Fig. 13.5 a Chemical structure, b coordinate system, and c room-temperature optical constants of PET. For the light polarization along the x, y, and z axes in b, the optical constants are defined by Nx = nx − ikx, Ny = ny − iky and Nz = nz − ikz. For the k spectra, only the in-plane components are shown. In c, the open circles show the experimental data and the solid lines indicate the calculation results obtained from the parameterization assuming the Tauc-Lorentz model expressed by (8.1) and (8.2). For the refractive index spectrum of nz, however, the Sellmeier model expressed by (13.1) was applied

Table 13.18 Tauc-Lorentz parameters of (8.1) and (8.2) for εx = (Nx)2 of PET Peak j j j j j j j

= = = = = = =

1 2 3 4 5 6 7

A (eV) 0.295 13.827 3.754 13.448 6.856 187.902 208.764

C (eV) −2

5.03 × 10 7.41 × 10−2 0.136 0.378 0.489 0.627 6.05 × 10−2

E0 (eV)

Eg (eV)

ε1(∞)

4.090 4.133 4.280 4.871 5.116 6.126 16.633

3.796 3.999 3.999 4.177 3.994 5.654 10.135

9.81 × 10−2 0 0 0 0 0 0

13

Substrates and Coating Layers

593

Table 13.19 Tauc-Lorentz parameters of (8.1) and (8.2) for εy = (Ny)2 of PET Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j j j

5.75 × 10−3 1.41 × 10−2 37.036 19.367 8.444 2.571 261.342 231.353

0.133 7.66 × 10−2 0.343 0.294 0.285 0.278 0.576 9.52 × 10−2

4.258 4.309 4.808 4.982 5.152 5.341 6.069 8.982

3.991 3.953 4.293 4.300 4.300 4.299 5.702 7.661

1.368 0 0 0 0 0 0 0

= = = = = = = =

1 2 3 4 5 6 7 8

Table 13.20 Sellmeier parameters of (13.1) for nz of PET Material

B2

B1

PET

0.888

0.282

C1 (μm2)

B3 –

9.18 × 10

C2 (μm2) −3

2.87 × 10

C3 (μm2) −2

–

Table 13.21 Optical constants of Nx = nx − ikx for PET reported by Hong et al. λ (nm)

nx

kx

λ (nm)

nx

kx

λ (nm)

nx

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420

1.806 1.802 1.775 1.760 1.749 1.740 1.733 1.726 1.720 1.715 1.710 1.705 1.701 1.698 1.694 1.691 1.688 1.685 1.682 1.679 1.677 1.672 1.668

5.65 × 10−2 6.61 × 10−3 3.00 × 10−4 5.3 × 10−5 9 × 10−6 2 × 10−6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760

1.640 1.638 1.637 1.636 1.635 1.633 1.632 1.631 1.630 1.630 1.629 1.628 1.627 1.626 1.626 1.625 1.624 1.624 1.623 1.623 1.622 1.622 1.621

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100

1.617 0 1.616 0 1.616 0 1.616 0 1.615 0 1.615 0 1.615 0 1.615 0 1.614 0 1.614 0 1.614 0 1.614 0 1.614 0 1.613 0 1.613 0 1.613 0 1.613 0 1.613 0 1.612 0 1.612 0 1.612 0 1.612 0 1.612 0 (continued)

kx

594

S. Fujimoto et al.

Table 13.21 (continued) λ (nm)

nx

kx

λ (nm)

nx

kx

λ (nm)

nx

kx

430 440 450 460 470 480 490 500 510 520 530

1.665 1.661 1.658 1.656 1.653 1.651 1.649 1.647 1.645 1.643 1.641

0 0 0 0 0 0 0 0 0 0 0

770 780 790 800 810 820 830 840 850 860 870

1.621 1.620 1.620 1.619 1.619 1.619 1.618 1.618 1.618 1.617 1.617

0 0 0 0 0 0 0 0 0 0 0

1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.612 1.611 1.611 1.611 1.611 1.611 1.611 1.610 1.610 1.610

0 0 0 0 0 0 0 0 0 0

ky

Table 13.22 Optical constants of Ny = ny − iky for PET reported by Hong et al. λ (nm) 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420

ny 1.878 1.861 1.847 1.834 1.823 1.813 1.804 1.796 1.789 1.782 1.776 1.771 1.765 1.760 1.756 1.752 1.748 1.744 1.740 1.737 1.734 1.728 1.723

ky −6

7 × 10 1 × 10−6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

λ (nm)

ny

ky

λ (nm)

ny

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760

1.687 1.685 1.683 1.682 1.680 1.679 1.678 1.676 1.675 1.674 1.673 1.672 1.671 1.670 1.669 1.669 1.668 1.667 1.666 1.666 1.665 1.664 1.664

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100

1.658 0 1.658 0 1.657 0 1.657 0 1.657 0 1.656 0 1.656 0 1.656 0 1.656 0 1.655 0 1.655 0 1.655 0 1.654 0 1.654 0 1.654 0 1.654 0 1.653 0 1.653 0 1.653 0 1.653 0 1.653 0 1.652 0 1.652 0 (continued)

13

Substrates and Coating Layers

595

Table 13.22 (continued) λ (nm)

ny

ky

λ (nm)

ny

ky

λ (nm)

ny

ky

430 440 450 460 470 480 490 500 510 520 530

1.718 1.714 1.710 1.707 1.703 1.700 1.698 1.695 1.693 1.691 1.689

0 0 0 0 0 0 0 0 0 0 0

770 780 790 800 810 820 830 840 850 860 870

1.663 1.663 1.662 1.662 1.661 1.661 1.660 1.660 1.659 1.659 1.659

0 0 0 0 0 0 0 0 0 0 0

1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.652 1.652 1.652 1.651 1.651 1.651 1.651 1.651 1.651 1.650

0 0 0 0 0 0 0 0 0 0

Table 13.23 Refractive index of nz for PET reported by Hong et al. (k = 0) λ (nm)

nz

λ (nm)

nz

λ (nm)

nz

λ (nm)

nz

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.5500 1.5468 1.5439 1.5411 1.5386 1.5361 1.5338 1.5317 1.5296 1.5277 1.5258 1.5241 1.5225 1.5209 1.5194 1.5180 1.5166 1.5153 1.5141 1.5129 1.5118 1.5097 1.5078 1.5060 1.5044 1.5029

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.5015 1.5001 1.4989 1.4978 1.4967 1.4958 1.4948 1.4940 1.4931 1.4924 1.4916 1.4910 1.4903 1.4897 1.4891 1.4886 1.4881 1.4876 1.4871 1.4866 1.4862 1.4858 1.4854 1.4851 1.4847 1.4844

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.4841 1.4837 1.4834 1.4832 1.4829 1.4826 1.4824 1.4821 1.4819 1.4817 1.4815 1.4813 1.4811 1.4809 1.4807 1.4805 1.4803 1.4802 1.4800 1.4799 1.4797 1.4796 1.4794 1.4793 1.4792 1.4790

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4789 1.4788 1.4787 1.4786 1.4785 1.4784 1.4783 1.4782 1.4781 1.4780 1.4779 1.4778 1.4777 1.4776 1.4775 1.4775 1.4774 1.4773 1.4772 1.4772 1.4771 1.4770 1.4770

596

S. Fujimoto et al.

13.2.6 PMMA [Poly(Methyl Methacrylate)] Data from N. Hong, R. A. Synowicki, and J. N. Hilfiker [5]. The optical data have been extracted from a commercial 130-μm-thick PMMA substrate (Plexiglas). The SE analysis has been performed assuming isotropic optical properties. The optical data of a PMMA thin film are shown in Fig. 9.14 (Fig. 13.6, Tables 13.24 and 13.25).

Fig. 13.6 a Chemical structure and b room-temperature optical constants of PMMA. The open circles show the reference data and the solid line indicates the refractive index spectrum calculated by the Sellmeier model of (13.1)

Table 13.24 Sellmeier parameters of (13.1) for PMMA Material

B1

B2

B3

C1 (μm2)

C2 (μm2)

C3 (μm2)

PMMA

1.179

2.56 × 10−3

3.67 × 10−2

1.02 × 10−2

5.42 × 10−2

14.528

Table 13.25 Optical constants of PMMA. The optical data reported by Hong et al. are shown λ (nm)

n

k ( × 10−4)

λ (nm)

n

k ( × 10−4)

300 305 310 315 320 325

1.5281 1.5262 1.5244 1.5227 1.5211 1.5196

2.57 2.47 2.29 2.19 2.28 2.55

540 550 560 570 580 590

1.4913 1.4907 1.4902 1.4897 1.4892 1.4888

0.06 0.06 0.06 0.06 0.06 0.06

λ (nm) 880 890 900 910 920 930

n

k ( × 10−4)

1.4817 1.4815 1.4814 1.4813 1.4811 1.4810

0.04 0.04 0.04 0.05 0.05 0.05 (continued)

13

Substrates and Coating Layers

597

Table 13.25 (continued) λ (nm)

n

k ( × 10−4)

λ (nm)

n

k ( × 10−4)

λ (nm)

n

k ( × 10−4)

330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.5182 1.5168 1.5156 1.5144 1.5133 1.5122 1.5112 1.5102 1.5092 1.5083 1.5074 1.5065 1.5057 1.5049 1.5041 1.5027 1.5014 1.5002 1.4991 1.4980 1.4971 1.4962 1.4953 1.4945 1.4938 1.4931 1.4924 1.4918

2.90 3.16 3.24 3.16 2.98 2.71 2.31 1.78 1.23 0.76 0.43 0.24 0.15 0.11 0.09 0.08 0.08 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.06 0.06 0.06

600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.4884 1.4880 1.4876 1.4872 1.4869 1.4866 1.4862 1.4859 1.4857 1.4854 1.4851 1.4849 1.4846 1.4844 1.4842 1.4839 1.4837 1.4835 1.4833 1.4831 1.4830 1.4828 1.4826 1.4824 1.4823 1.4821 1.4820 1.4818

0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4809 1.4808 1.4807 1.4805 1.4804 1.4803 1.4802 1.4801 1.4800 1.4799 1.4798 1.4797 1.4796 1.4795 1.4794 1.4794 1.4793 1.4792 1.4791 1.4790 1.4789 1.4788 1.4788 1.4787 1.4786 1.4785 1.4785

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.08 0.09 0.11 0.13 0.13 0.12 0.10

13.2.7 Polyimide Data from M. Campoy-Quiles, J. Nelson, D. D. C. Bradley and P. G. Etchegoin [6]. The optical data have been extracted from a polyimide thin film prepared by a spin coating process. In this process, a precursor solution (polyamic acid) was coated onto a fused silica substrate, followed by thermal annealing. The SE analysis has been performed assuming isotropic optical properties (Fig. 13.7, Tables 13.26 and 13.27).

598

S. Fujimoto et al.

Fig. 13.7 Optical constants of polyimide at room temperature. The open circles show the reference data and the solid lines indicate the calculation result obtained from the parameterization assuming the Tauc-Lorentz model [(8.1) and (8.2)]

Table 13.26 Tauc-Lorentz parameters of (8.1) and (8.2) for polyimide Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j=1 j=2

0.693 10.639

0.570 0.109

4.434 5.036

1 × 10−4 2.756

1.947 0

Table 13.27 Optical constants of polyimide calculated by the Tauc-Lorentz model λ (nm)

n

k

λ (nm)

n

k

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370

1.985 1.957 1.930 1.905 1.883 1.862 1.844 1.828 1.813 1.800 1.788 1.777 1.767 1.758 1.750

0.159 0.128 0.104 8.63 × 7.27 × 6.22 × 5.38 × 4.72 × 4.17 × 3.72 × 3.35 × 3.03 × 2.76 × 2.53 × 2.33 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680

1.642 1.640 1.638 1.636 1.634 1.632 1.630 1.629 1.627 1.626 1.625 1.623 1.622 1.621 1.620

5.86 5.62 5.40 5.19 5.00 4.82 4.66 4.51 4.36 4.23 4.11 3.99 3.88 3.78 3.68

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

× × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020

1.607 1.607 1.606 1.606 1.606 1.605 1.605 1.605 1.604 1.604 1.604 1.603 1.603 1.603 1.603

2.45 × 10−3 2.41 × 10−3 2.38 × 10−3 2.34 × 10−3 2.30 × 10−3 2.27 × 10−3 2.24 × 10−3 2.20 × 10−3 2.17 × 10−3 2.14 × 10−3 2.11 × 10−3 2.09 × 10−3 2.06 × 10−3 2.03 × 10−3 2.01 × 10−3 (continued)

13

Substrates and Coating Layers

599

Table 13.27 (continued) λ (nm)

n

k

375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.742 1.735 1.729 1.723 1.717 1.712 1.703 1.695 1.687 1.681 1.675 1.670 1.665 1.661 1.657 1.654 1.650 1.647 1.645

2.16 2.00 1.87 1.75 1.64 1.55 1.38 1.25 1.14 1.05 9.72 9.06 8.48 7.97 7.52 7.11 6.75 6.43 6.13

× × × × × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.619 1.618 1.617 1.616 1.616 1.615 1.614 1.614 1.613 1.612 1.612 1.611 1.610 1.610 1.609 1.609 1.608 1.608 1.608

3.59 3.50 3.41 3.34 3.26 3.19 3.12 3.05 2.99 2.93 2.88 2.82 2.77 2.72 2.67 2.62 2.58 2.53 2.49

× × × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

λ (nm)

n

k

1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.602 1.602 1.602 1.602 1.601 1.601 1.601 1.601 1.601 1.600 1.600 1.600 1.600 1.600 1.600 1.599 1.599 1.599

1.98 1.96 1.93 1.91 1.89 1.86 1.84 1.82 1.80 1.78 1.76 1.74 1.72 1.70 1.69 1.67 1.65 1.63

× × × × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

13.2.8 Kapton HN [Poly{N,N’-(Oxydiphenylene) Pyromellitimide}] Data from N. Hong, R. A. Synowicki, and J. N. Hilfiker [5]. Kapton HN (DuPont Teijin Films) is a polyimide-based compound (see Fig. 13.8a) and the biaxial optical anisotropy of a 50-μm-thick Kapton HN substrate has been characterized by Mueller-matrix SE in reflection and transmission modes. Full SE data sets obtained at different incident and sample rotation angles were analyzed to extract the optical data. The biaxial material has different optical constants for polarizations along the x, y, and z axes: i.e., Nx = nx − ikx, Ny = ny − iky, and Nz = nz − ikz. For the z direction, however, only the non-absorbing region has been characterized assuming kz = 0. In the case of a Kapton HN substrate, the light absorption in the substrate can be estimated as an average of kx and ky, as the electric fields of incident light can be decomposed into the components parallel to the x and y axes (see also Fig. 13.8b). The optical properties of a Kapton H film [7] are quite similar to those of the Kapton HN (Tables 13.28, 13.29, 13.30, 13.31, 13.32 and 13.33).

600

S. Fujimoto et al.

Fig. 13.8 a Chemical structure, b coordinate system, and c room-temperature optical constants of Kapton HN. For the light polarization along the x, y, and z axes in b, the optical constants are defined by Nx = nx − ikx, Ny = ny − iky and Nz = nz − ikz. For the k spectra, only the in-plane components are shown. In c, the open circles show the experimental data and the solid lines indicate the calculation results obtained from the parameterization assuming the Tauc-Lorentz model expressed by (8.1) and (8.2). For the refractive index spectrum of nz, however, the Sellmeier model expressed by (13.1) was applied

Table 13.28 Tauc-Lorentz parameters of (8.1) and (8.2) for εx = (Nx)2 of Kapton HN Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j j

6.16 × 10−2 4.77 × 10−2 4.912 14.727 60.075 0.647

0.210 0.303 0.600 0.720 0.888 0.273

3.046 3.201 3.440 4.205 5.059 5.967

2.793 2.654 3.007 3.200 4.338 4.525

2.322 0 0 0 0 0

= = = = = =

1 2 3 4 5 6

13

Substrates and Coating Layers

601

Table 13.29 Tauc-Lorentz parameters of (8.1) and (8.2) for εy = (Ny)2 of Kapton HN Peak

A (eV)

C (eV)

E0 (eV)

Eg (eV)

ε1(∞)

j j j j j

1.29 × 10−2 4.268 13.826 61.403 2.757

0.162 0.608 0.645 0.986 0.240

3.053 3.543 4.216 5.053 6.006

2.727 3.014 3.175 4.272 5.425

2.283 0 0 0 0

= = = = =

1 2 3 4 5

Table 13.30 Sellmeier parameters of (13.1) for nz of Kapton HN Material

B2

B1

Kapton HN

0.752

B3

0.795

–

C1 (μm2)

C2 (μm2) −3

C3 (μm2) −2

5.83 × 10

–

1.96 × 10

Table 13.31 Optical constants of Nx = nx − ikx for Kapton HN reported by Hong et al. λ (nm)

nx

kx

λ (nm)

nx

kx

λ (nm)

nx

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420

1.971 1.989 1.992 1.984 1.969 1.951 1.934 1.919 1.909 1.901 1.895 1.890 1.884 1.877 1.869 1.861 1.853 1.844 1.836 1.829 1.822 1.810 1.801

0.281 0.236 0.192 0.152 0.121 9.94 × 8.50 × 7.58 × 6.91 × 6.29 × 5.60 × 4.82 × 3.98 × 3.16 × 2.40 × 1.76 × 1.24 × 8.40 × 5.52 × 3.52 × 2.18 × 7.78 × 2.55 ×

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760

1.757 1.754 1.753 1.751 1.749 1.747 1.746 1.745 1.743 1.742 1.741 1.740 1.739 1.738 1.737 1.736 1.735 1.735 1.734 1.733 1.733 1.732 1.731

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100

1.726 0 1.725 0 1.725 0 1.725 0 1.724 0 1.724 0 1.724 0 1.724 0 1.723 0 1.723 0 1.723 0 1.722 0 1.722 0 1.722 0 1.722 0 1.722 0 1.721 0 1.721 0 1.721 0 1.721 0 1.721 0 1.720 0 1.720 0 (continued)

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−4 10−4

kx

602

S. Fujimoto et al.

Table 13.31 (continued) λ (nm)

nx

kx

λ (nm)

nx

kx

λ (nm)

nx

kx

430 440 450 460 470 480 490 500 510 520 530

1.793 1.787 1.781 1.776 1.772 1.768 1.764 1.761 1.758 1.756 1.753

7.8 × 10−5 2.2 × 10−5 6 × 10−6 2 × 10−6 0 0 0 0 0 0 0

770 780 790 800 810 820 830 840 850 860 870

1.731 1.730 1.730 1.729 1.729 1.728 1.728 1.727 1.727 1.727 1.726

0 0 0 0 0 0 0 0 0 0 0

1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.720 1.720 1.720 1.719 1.719 1.719 1.719 1.719 1.719 1.719

0 0 0 0 0 0 0 0 0 0

Table 13.32 Optical constants of Ny = ny − iky for Kapton HN reported by Hong et al. λ (nm)

ny

ky

λ (nm)

ny

ky

λ (nm)

ny

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420

2.003 2.021 2.021 2.008 1.988 1.968 1.950 1.938 1.929 1.922 1.916 1.908 1.899 1.890 1.879 1.869 1.859 1.850 1.841 1.834 1.827 1.816 1.807

0.3 0.247 0.196 0.153 0.122 0.101 8.86 × 10−2 7.99 × 10−2 7.19 × 10−2 6.29 × 10−2 5.27 × 10−2 4.21 × 10−2 3.20 × 10−2 2.31 × 10−2 1.59 × 10−2 1.04 × 10−2 6.57 × 10−3 3.99 × 10−3 2.33 × 10−3 1.32 × 10−3 7.25 × 10−4 2.02 × 10−4 5.1 × 10−5

540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760

1.687 1.685 1.683 1.682 1.680 1.679 1.678 1.676 1.675 1.674 1.673 1.672 1.671 1.670 1.669 1.669 1.668 1.667 1.666 1.666 1.665 1.664 1.664

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100

1.658 0 1.658 0 1.657 0 1.657 0 1.657 0 1.656 0 1.656 0 1.656 0 1.656 0 1.655 0 1.655 0 1.655 0 1.654 0 1.654 0 1.654 0 1.654 0 1.653 0 1.653 0 1.653 0 1.653 0 1.653 0 1.652 0 1.652 0 (continued)

ky

13

Substrates and Coating Layers

603

Table 13.32 (continued) λ (nm)

ny

ky

λ (nm)

ny

ky

λ (nm)

ny

ky

430 440 450 460 470 480 490 500 510 520 530

1.799 1.793 1.787 1.782 1.778 1.774 1.770 1.767 1.764 1.761 1.759

1.2 × 10−5 3 × 10−6 1 × 10−6 0 0 0 0 0 0 0 0

770 780 790 800 810 820 830 840 850 860 870

1.663 1.663 1.662 1.662 1.661 1.661 1.660 1.660 1.659 1.659 1.659

0 0 0 0 0 0 0 0 0 0 0

1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.652 1.652 1.652 1.651 1.651 1.651 1.651 1.651 1.651 1.650

0 0 0 0 0 0 0 0 0 0

Table 13.33 Refractive index of nz for Kapton HN reported by Hong et al. (k = 0) λ (nm)

nz

λ (nm)

nz

λ (nm)

nz

λ (nm)

nz

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.6792 1.6759 1.6728 1.6700 1.6673 1.6647 1.6623 1.6600 1.6578 1.6558 1.6538 1.6520 1.6502 1.6486 1.6470 1.6455 1.6440 1.6426 1.6413 1.6400 1.6388 1.6366 1.6345 1.6325 1.6308 1.6291

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.6276 1.6262 1.6248 1.6236 1.6224 1.6213 1.6203 1.6194 1.6185 1.6176 1.6168 1.6161 1.6154 1.6147 1.6140 1.6134 1.6129 1.6123 1.6118 1.6113 1.6108 1.6104 1.6099 1.6095 1.6091 1.6088

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.6084 1.6081 1.6077 1.6074 1.6071 1.6068 1.6066 1.6063 1.6060 1.6058 1.6055 1.6053 1.6051 1.6049 1.6047 1.6045 1.6043 1.6041 1.6039 1.6037 1.6036 1.6034 1.6033 1.6031 1.6030 1.6028

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.6027 1.6026 1.6024 1.6023 1.6022 1.6021 1.6019 1.6018 1.6017 1.6016 1.6015 1.6014 1.6013 1.6012 1.6011 1.6011 1.6010 1.6009 1.6008 1.6007 1.6006 1.6006 1.6005

604

S. Fujimoto et al.

13.2.9 EVA [Ethylene Vinyl Acetate] Data from (i) K. R. McIntosh, G. Lau, J. N. Cotsell, K. Hanton, D. L. Bätzner, F. Bettiol and B. S. Richards [8], (ii) K. R. McIntosh, J. N. Cotsell, J. S. Cumpston, A. W. NorrisN. E. Powell, and B. M. Ketola [9] (Fig. 13.9, Tables 13.34 and 13.35).

Fig. 13.9 a Chemical structure and b room-temperature optical constants of EVA. The open circles show the reference data and the solid line indicates the refractive index spectrum calculated by the Sellmeier model of (13.1)

Table 13.34 Sellmeier parameters of (13.1) for EVA Material

B1

B2

B3

C1 (μm2)

C2 (μm2)

C3 (μm2)

EVA

1.210

7.65 × 10−3

16.358

4.84 × 10−3

7.35 × 10−2

580.829

Table 13.35 Refractive index of EVA calculated by the Sellmeier model. The extinction coefficient reported by McIntosh et al. is also shown λ (nm)

n

300 305 310 315 320

1.5225 1.5199 1.5179 1.5162 1.5147

k ( × 10−5)

λ (nm)

n

k ( × 10−5)

15.3840

540 550 560 570 580

1.4941 1.4937 1.4934 1.4930 1.4926

0.0243 0.0236 0.0230 0.0228 0.0223

λ (nm) 880 890 900 910 920

n

k ( × 10−5)

1.4847 1.4844 1.4842 1.4840 1.4837

0.0146 0.0245 0.0337 0.0483 0.0807 (continued)

13

Substrates and Coating Layers

605

Table 13.35 (continued) λ (nm)

n

k ( × 10−5)

λ (nm)

n

k ( × 10−5)

λ (nm)

n

k ( × 10−5)

325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450 460 470 480 490 500 510 520 530

1.5134 1.5122 1.5111 1.5102 1.5093 1.5085 1.5077 1.5070 1.5063 1.5057 1.5051 1.5045 1.5039 1.5034 1.5029 1.5025 1.5016 1.5008 1.5000 1.4993 1.4986 1.4980 1.4974 1.4969 1.4964 1.4959 1.4954 1.4950 1.4945

16.8150 17.0840 17.3430 17.5670 16.4910 14.5010 12.9930 11.4320 9.7343 6.4349 3.8936 2.2007 1.2961 0.7669 0.4565 0.2822 0.1237 0.0701 0.0480 0.0403 0.0360 0.0330 0.0312 0.0299 0.0287 0.0275 0.0264 0.0256 0.0249

590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870

1.4923 1.4920 1.4916 1.4913 1.4910 1.4907 1.4904 1.4901 1.4899 1.4896 1.4893 1.4890 1.4888 1.4885 1.4883 1.4880 1.4878 1.4875 1.4873 1.4870 1.4868 1.4865 1.4863 1.4861 1.4858 1.4856 1.4854 1.4851 1.4849

0.0216 0.0210 0.0205 0.0200 0.0196 0.0193 0.0190 0.0185 0.0177 0.0169 0.0160 0.0146 0.0137 0.0135 0.0136 0.0135 0.0134 0.0124 0.0114 0.0105 0.0095 0.0088 0.0087 0.0086 0.0087 0.0088 0.0089 0.0093 0.0106

930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.4835 1.4833 1.4830 1.4828 1.4826 1.4823 1.4821 1.4819 1.4816 1.4814 1.4812 1.4809 1.4807 1.4804 1.4802 1.4800 1.4797 1.4795 1.4792 1.4790 1.4787 1.4785 1.4782 1.4780 1.4777 1.4775 1.4772 1.4770

0.1038 0.0661 0.0296 0.0181 0.0146 0.0137 0.0161 0.0220 0.0321 0.0402 0.0490 0.0576 0.0529 0.0415 0.0323 0.0273 0.0230 0.0215 0.0249 0.0342 0.0545 0.0990 0.1821 0.3301 0.4595 0.6129 0.8518 1.2670

13.2.10

MgF2, LiF and NaF

The refractive index spectra of MgF2, LiF and NaF materials reported in the following references are parameterized by the Sellmeier model of (13.1) and the modeled results are summarized: (i) MgF2: unpublished results of S. Fujimoto, (ii) LiF: E. D. Palik [10], (iii) NaF: E. D. Palik [11] (Fig. 13.10, Tables 13.36, 13.37, 13.38 and 13.39).

606

S. Fujimoto et al.

Fig. 13.10 Refractive index spectra of MgF2, LiF and NaF calculated by the Sellmeier model of (13.1)

Table 13.36 Sellmeier parameters of (13.1) for MgF2, LiF and NaF Material

B1

MgF2 LiF NaF

0.896 0.926 0.207

B2 0.699 7.045 0.536

B3 – – 0.424

C1 (μm2) −3

6.73 × 10 5.44 × 10−3 1.07 × 10−5

C2 (μm2)

C3 (μm2)

127.462 1087.014 9.05 × 10−3

– – 251.444

Table 13.37 Refractive index of MgF2 calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370

1.4028 1.4019 1.4011 1.4002 1.3995 1.3987 1.3980 1.3973 1.3967 1.3961 1.3955 1.3949 1.3944 1.3939 1.3934

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

1.3872 1.3867 1.3863 1.3858 1.3854 1.3851 1.3847 1.3844 1.3840 1.3837 1.3834 1.3832 1.3829 1.3827 1.3824

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860

1.3802 1.3800 1.3799 1.3798 1.3796 1.3795 1.3794 1.3792 1.3791 1.3790 1.3789 1.3788 1.3787 1.3786 1.3785

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120

n 1.3773 1.3772 1.3772 1.3771 1.3770 1.3769 1.3768 1.3767 1.3767 1.3766 1.3765 1.3764 1.3763 1.3763 1.3762 (continued)

13

Substrates and Coating Layers

607

Table 13.37 (continued) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

375 380 385 390 395 400 410 420 430 440 450

1.3929 1.3925 1.3920 1.3916 1.3912 1.3909 1.3901 1.3895 1.3888 1.3882 1.3877

610 620 630 640 650 660 670 680 690 700 710

1.3822 1.3820 1.3818 1.3816 1.3814 1.3812 1.3810 1.3808 1.3807 1.3805 1.3803

870 880 890 900 910 920 930 940 950 960 970

1.3784 1.3783 1.3782 1.3781 1.3780 1.3779 1.3778 1.3777 1.3776 1.3775 1.3774

1130 1140 1150 1160 1170 1180 1190 1200

1.3761 1.3760 1.3760 1.3759 1.3758 1.3757 1.3757 1.3756

Table 13.38 Refractive index of LiF calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.4089 1.4082 1.4075 1.4068 1.4062 1.4056 1.4050 1.4044 1.4039 1.4034 1.4029 1.4025 1.4020 1.4016 1.4012 1.4008 1.4005 1.4001 1.3998 1.3994 1.3991 1.3985 1.3980 1.3975 1.3970 1.3965

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.3961 1.3957 1.3953 1.3950 1.3946 1.3943 1.3940 1.3937 1.3935 1.3932 1.3930 1.3927 1.3925 1.3923 1.3921 1.3919 1.3917 1.3915 1.3913 1.3912 1.3910 1.3908 1.3907 1.3905 1.3904 1.3903

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.3901 1.3900 1.3899 1.3897 1.3896 1.3895 1.3894 1.3893 1.3892 1.3891 1.3890 1.3888 1.3887 1.3886 1.3885 1.3885 1.3884 1.3883 1.3882 1.3881 1.3880 1.3879 1.3878 1.3877 1.3876 1.3875

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.3875 1.3874 1.3873 1.3872 1.3871 1.3870 1.3870 1.3869 1.3868 1.3867 1.3866 1.3866 1.3865 1.3864 1.3863 1.3862 1.3862 1.3861 1.3860 1.3859 1.3859 1.3858 1.3857

608

S. Fujimoto et al.

Table 13.39 Refractive index of NaF calculated by the Sellmeier model (k = 0) λ (nm)

n

λ (nm)

n

λ (nm)

n

λ (nm)

n

300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 410 420 430 440 450

1.3427 1.3419 1.3411 1.3404 1.3397 1.3391 1.3384 1.3379 1.3373 1.3368 1.3363 1.3358 1.3353 1.3349 1.3344 1.3340 1.3336 1.3333 1.3329 1.3326 1.3322 1.3316 1.3311 1.3305 1.3300 1.3296

460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710

1.3291 1.3287 1.3284 1.3280 1.3277 1.3274 1.3271 1.3268 1.3265 1.3263 1.3260 1.3258 1.3256 1.3254 1.3252 1.3250 1.3249 1.3247 1.3245 1.3244 1.3243 1.3241 1.3240 1.3239 1.3237 1.3236

720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970

1.3235 1.3234 1.3233 1.3232 1.3231 1.3230 1.3229 1.3228 1.3227 1.3226 1.3226 1.3225 1.3224 1.3223 1.3223 1.3222 1.3221 1.3221 1.3220 1.3219 1.3219 1.3218 1.3218 1.3217 1.3216 1.3216

980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200

1.3215 1.3215 1.3214 1.3214 1.3213 1.3213 1.3212 1.3212 1.3212 1.3211 1.3211 1.3210 1.3210 1.3209 1.3209 1.3209 1.3208 1.3208 1.3207 1.3207 1.3207 1.3206 1.3206

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

R.A. Synowicki, B.D. Johs, A.C. Martin, Thin Solid Films 519, 2907 (2011) SCHOTT optical glass data sheets (2012) I.H. Malitson, J. Opt. Soc. Am. 55, 1205 (1965) G. Gosh, Opt. Commun. 163, 95 (1999) N. Hong, R.A. Synowicki, J.N. Hilfiker, Appl. Surf. Sci. 421, 518 (2017) M. Campoy-Quiles, J. Nelson, D.D.C. Bradley, P.G. Etchegoin, Phys. Rev. B 76, 235206 (2007) E.T. Arakawa, M.W. Williams, J.C. Ashley, L.R. Painter, J. Appl. Phys. 52, 3579 (1981) K.R. McIntosh, G. Lau, J.N. Cotsell, K. Hanton, D.L. Bätzner, F. Bettiol, B.S. Richards, Prog. Photovoltaics 17, 191 (2009) K.R. McIntosh, J.N. Cotsell, J.S. Cumpston, A.W. Norris, N.E. Powell, B.M. Ketola, in Proceeding of the 34th IEEE PVSC (IEEE, New York, 2009), p. 544 E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985) E.D. Palik, Handbook of Optical Constants of Solids II (Academic Press, New York, 1991)

Index

A Absorbance, 183 Absorbance spectroscopy, 110 Absorber layer thickness, 241 Absorber layer thickness reduction, 243 Absorptance, 22, 40 Absorption coefficient, 8, 89, 256 Absorption loss, 23, 48, 76 Absorption onset, 88 Absorption spectrum, 320 Absorption tail, 9 AES depth profile, 232 Ag, 170, 545, 550 Air-mass 1.5 global, 3 Al, 545, 552 Al2O3, 329 AlAs, 9, 356 Alloy composition, 214 AlSb, 367 Ambient/glass interface, 103 AM1.5G, 3, 41 Amorphous semiconductor, 260 Amorphous silicon (a-Si:H), 338, 340 Amorphous silicon carbide (a-SiC:H), 346 Amorphous silicon oxide (a-SiO:H), 350 Amorphous-to-(mixed-phase) transition, 310 Angle of incidence, 191, 222 Angle of incidence calibration, 191 Anisotropy, 428 Annealing, 99 Anti-Reflection Coating (ARC), 85, 225 Anti-reflection layer, 21, 575 APFO-3, 429 APFO-Green9, 431

ARC method, 35, 46 Asahi-U, 63, 151 A-Si:H, 9, 19, 83, 170, 225, 338, 340 A-Si:H/c-Si heterojunction solar cell, 72, 143 A-Si:H local network model, 147 A-Si:H n-i-p solar cell, 170 A-Si:H n-layer, 170 A-Si:H solar cell, 63, 158 A-SiO:H/c-Si, 19 A-Si1-xCx:H, 264, 346 Asymmetric double-Gaussian profile, 45 Atmospheric pressure vapor deposition, 176 Au, 545, 554 Au back contact, 102 Auger Electron Spectroscopy (AES), 119, 232 B Back contact, 84 Back reflector, 78, 170 Back-side reflection, 543 Back-Surface Field (BSF), 22, 49, 78 Band filling, 107 Band gap, 89, 199, 256 Band gap energies, 172 Band gap profile, 236 Band offset, 59 Band structure critical points, 261 Beam focusing, 174 Beer’s law, 50 Biaxial optical anisotropy, 575 Birefringence, 174 Borosilicate glass, 577 Broadening, 172 Broadening parameter, 89, 270

© Springer International Publishing AG, part of Springer Nature 2018 H. Fujiwara and R. W. Collins (eds.), Spectroscopic Ellipsometry for Photovoltaics, Springer Series in Optical Sciences 214, https://doi.org/10.1007/978-3-319-95138-6

609

610 Bruggeman Effective Medium Approximation (EMA), 88, 178, 227 B-spline, 215 Built-in electric field, 94 Bulk layer, 104, 214 Bulk layer thickness, 179, 259 Burstein-Moss effect, 118 Burstein-Moss shift, 48 C Cadmium telluride, 83 Calibration, 189 Camera, 189 Carrier collection, 83 Carrier collection efficiency, 50 Carrier collection length, 23, 50 Carrier collection profile, 94 Carrier continuity equation, 51 Carrier diffusion, 51 Carrier drift, 51 Carrier loss, 76 Carrier loss mechanism, 74 Carrier recombination, 31, 50 CdCl2 treatment, 99 CdS, 99, 174, 374 CdS/CdTe heterojunction, 98 CdS/CdTe interface, 106, 178 CdS/CdTe PV panel, 174 CdSe, 376 CdS effective thickness, 181 CdS layer, 174 CdS window layer, 174 CdS1–xTex, 101 CdTe, 5, 11, 19, 83, 169, 378 CdTe PV module, 169 CdTe solar cell, 61, 178 C (graphite), 556 CH3NH3PbI3, 5, 9, 19, 475 CH3NH3PbI3 solar cell, 75 CH3NH3I, 491 Characterization of Textured Structures, 139 Charge carrier collection, 183 Chemical bath deposition, 113 CIGS, 83, 209 CIGS/CdS interface, 122 CIGS deposition process, 214 CIGSe, 9, 19, 547 CIGSe solar cell, 21, 43, 140, 164 CIGS solar cell, 113, 212 CISe, 16

Index Close-space sublimation, 99 Coalescence, 229 Coating layer, 575 Cody-Lorentz oscillator, 88, 201, 280 Coevaporation, 209 Coherent condition, 41 Coherent length, 41, 67 Collection grids, 118 Collection probability profile, 127 Complex amplitude reflection ratio, 103 Complex dielectric constant, 8 Complex dielectric function, 84, 186, 211, 255 Complex refractive index, 8 Composition, 230 Compositional gradient, 234 Composition profile, 116, 214 Compressive stress, 108 Confidence limits, 103 Conical nanocrystallites, 309 Continuous Phase Approximation (CPA), 67 Conversion efficiency, 2 Copper indium-gallium diselenide, 83, 209 Copper Phthalocyanine (CuPc), 431 Copper selenide, 209 Cr, 194, 558 Critical point, 100 Critical Point (CP) oscillator, 116, 198, 217 Cross-sectional transmission electron micrograph, 109 Crystalline grain structure, 267 Crystalline silicon, 296 C-Si, 548 C-Si heterojunction solar cell, 69 C-Si solar cell, 66 Cu, 560 CuGaSe2, 382 Cu(In,Ga)Se2 (CIGSe), 5 CuIn1−xGaxSe2, 83, 209, 384, 547 CuIn1–xGaxSe2 (CIGS) solar cell, 185 CuInSe2, 380 Cu2SnSe3, 413 Cu2ZnGeSe4, 411 Cu2ZnSnS4 (CZTS), 5, 401 Cu2ZnSnSe4 (CZTSe), 5, 402 Cu2ZnSn(S,Se)4 (CZTSSe), 5 Cu2ZnSn(SxSe1−x)4, 405 Cu2−xSe, 209 Cu deficient CIGS, 225 Cu-poor CIGS, 232 Cu-rich CIGS, 232

Index Current density, 110 Current-density-voltage (J-V) measurements, 304 Curvature model, 151 CZTS, 9 CZTSe, 9 CZTSe solar cell, 53 CZTSSe solar cell, 22 CZTS solar cell, 58 D Data analysis, 84 Database dielectric function, 227 Dead layer, 57 Defect complex, 235 Degenerate doping, 118 Depletion layer thickness, 51 Deposition rate, 210, 260 Deposition system, 194 Depth profile, 260 Dielectric function, 8, 83, 178, 255 Dielectric function database, 115 Dielectric function gradient, 234 Dielectric function modeling, 12 Diffusion barrier, 186 Diffusion coefficient, 238 Diffusion length, 51 Dipolar plasmon, 200 Dipole matrix element, 201 Direct-transition semiconductor, 9 Disorder, 92, 171 Doped window layer, 96 Doping, 92 DPPTTT, 467 Drude component, 262 Drude free electron, 116, 217 Drude free electron formula, 196 Drude model, 47, 496 E Eagle XG glass, 577 e-ARC method, 50 e-ERS, 53 Effective mass, 497 Effective medium approximation, 260 Effective medium layer, 182 Effective thickness, 92, 174, 256 Efficiency, 7, 86, 225 Electromagnetic wave, 36 Electron, 102 Electron beam evaporation, 113

611 Electron concentration, 107 Electron-hole recombination, 84 Electronic loss, 85 Electronic transition, 171 Electron impact emission spectroscopy, 113 Electron mean free time, 196 Electron-volt, 4 Elementary cell, 141 Ellipsometer translation, 180 Ellipsometry angles, 189 EMA multilayer model, 151 Emissivity, 225 End-point detection, 113, 213 Energy Dispersive X-ray Spectroscopy (EDS), 117, 218 Energy shift model, 384, 405, 479 EQE analysis, 30 EQE characteristics, 19 EQE limit, 20 Error function, 118 ERS method, 35, 43 Ethylene Vinyl Acetate (EVA), 604 Evaporation rate, 222 Exact inversion, 88 Excited carrier mean free path, 109 Expanded beam spectroscopic ellipsometer, 187 Expanded probe beam, 186 Ex-situ spectroscopic ellipsometry, 83 Extended ARC method, 50 External Quantum Efficiency (EQE), 29, 83, 172 Extinction coefficient, 8 Extraordinary ray, 428 F FAPbI3 (a phase), 473 FAPbI3 (d phase), 487 F doping, 107 Fill-factor, 2, 94, 225, 289 Fitting error function, 153 Flexible substrate, 186 Flexible thin film photovoltaic (PV) modules, 185 Formamidinium lead iodide FAPbI3(HC (NH2)2PbI3), 471, 473, 547 Free carrier absorption, 47, 496, 545 Fresnel coefficients, 191 F8TBT, 429 Full-size PV panel, 173 Fused silica, 577

612 G GaAs, 6, 12, 358 Ga2O3, 331 GaP, 9, 363 Ge, 9, 325 Glass/film-stack interface, 103 Glass-side illumination, 158 Grain boundaries, 232, 258 Grain boundary scattering, 108 Grain growth, 213 Grain size, 108 Graphene, 498 Grids, 113 Growth evolution diagram, 255 Growth mechanism, 212 H H2 dilution, 93 Heterojunction, 178 Heterojunction interface, 124 Heterojunction solar cell, 68 High Resistivity Transparent (HRT) layer, 99, 176 Hole diffusion length, 94 HRT layer, 106 Hybrid perovskite, 471, 548 Hydrogenated amorphous, 86 Hydrogenated amorphous silicon, 83, 170, 256 Hydrogenated nanocrystalline silicon, 256 Hydrogenated silicon, 186, 255 Hydrogen incorporation, 93 I Ideal collection, 124 Imaging, 186 Imaging/mapping SE, 186 Imaging multichannel SE, 172 Imaging spectrograph, 189 Inactive layer, 94 InAs, 360 Incoherent condition, 41 Incoherent light absorption, 66 Incoherent summation, 104 Index of refraction, 200 Indirect bandgap, 261 Indirect-transition semiconductor, 9 Indium-gallium selenide, 209 Inorganic Semiconductor, 319 InP, 12, 365 In-plane strain, 171

Index In2S3, 418 In2O3:H, 502 In2O3 (non-doped), 500 In2O3:Sn, 504, 506, 508 In situ monitoring, 213 In situ SE, 216 Instantaneous deposition rate, 241 Interband CP transition, 102 Inter-diffusion, 178 Interface, 83, 259 Interface formation, 212 Interface layer, 91, 179, 264 Interface layer composition, 104 Interface roughness, 118, 178, 198, 215, 264 Interference fringe pattern, 230 Internal quantum efficiency, 31 Intraband transition, 101 Intrinsic absorber layer, 86 Inversion, 214, 260 (In1-xGax)2Se3, 113, 209 InZnO, 510 IQE, 31 Irradiance, 3, 36 ITO, 504, 506, 508 J Junction, 84 (J-V) characteristic, 114 K Kapton HN [poly{N,N’-(oxydiphenylene) pyromellitimide}], 599 Kramers-Kronig consistent, 217 Kramers-Kronig integration, 321, 497 L Lamp, 189 Law of the minimum, 30 Layer thickness, 172 Least-squares regression, 219 Least squares regression analysis, 83, 260 Levenberg-Marquardt algorithm, 103 LiF, 605 Light absorption, 18 Light scattering, 34, 94 Light trapping, 85 Light trapping gain, 96 Linear detector array, 171 Lorentz oscillator, 88, 198, 219, 261

Index M Magnetron sputtering, 99, 178 Maximum Jsc, 5 MAPbBr3 (CH3NH3PbBr3), 477 MAPbCl3 (CH3NH3PbCl3), 485 MAPb(I1-xBrx)3 (CH3NH3Pb(I1-xBrx)3), 479 Mapping, 136 Mapping SE, 192, 304 Material density, 171 Matrix element, 88 Maximum efficiency, 7 Maxwell’s equations, 8 Mean free time, 102 Mean Square Error (MSE), 103, 195, 217, 281 Metal, 84, 543 Methylammonium lead iodide MAPbI3(CH3NH3PbI3), 471, 475 Mg, 562 MgF2, 119, 605 MgF2 ARC, 119 MgF2 biplate, 188 Microcrystalline Si (lc-Si:H), 354 Micromorph tandem, 256 Mixed phase a-Si-H + nc-Si:H, 260 Mixed-phase-to-nanocrystalline transition, 299 Mo, 545, 564 Mo back contact, 114 Mobility, 102 Mo-coated, 209 Molybdenum, 113, 249 MoS2, 217, 419 MoSe2 (polycrystal), 421 MoSe2 (single crystal), 423 MoOx, 512 Mueller-matrix SE, 587 Multichannel ellipsometer, 84, 175 Multichannel spectroscopic ellipsometer, 171, 213 Multijunction thin film PV, 256 Multilayer analysis, 83 Multilayer model, 181 Multi-sample analysis, 91 Multi-sample model, 91 Multi-step analysis, 104 Multi-time analysis, 116, 214, 265 N NaF, 605 Nanocrystalline material, 218 Nanocrystalline volume fraction, 256 Nanocrystals, 281

613 Nc-Si:H, 255 Ni, 545, 566 NiO, 515 Non-doped TCO, 495 Non-invasive analysis, 109 Non-linear least-squares regression, 172 Nonparabolic TCO conduction band, 497 n-type a-Si:H, 88 n-type hydrogenated amorphous silicon, 186 n-type nc-Si-H, 304 n-type Si-H, 255 Nucleation, 257 Nucleation density, 282 O Off-line SE mapping, 174 One-stage coevaporation, 220 On-line mapping, 169 On-line monitoring, 169 On-line SE, 173 Open-circuit voltage, 2, 92, 179, 225, 306 Optical admittance, 38 Optical admittance method, 36 Optical carrier concentration, 497 Optical constants, 8 Optical gain, 47 Optical loss, 76, 83 Optical mobility, 497 Optical model, 226 Optical properties, 84 Optical properties of metal, 545 Optical simulation, 83 Ordinary ray, 428 Organic-inorganic hybrid perovskite, 471 Organic semiconductors, 427 Oscillator amplitude, 172 Oscillator model, 85 Oxidation, 214 P Parameterization, 220 Parameter map, 203 Parameter reduction, 268 Parametric model, 227 Parasitic absorption, 24, 547 Parasitic light absorption, 31 Partial EQE, 21, 49 Passivation layer, 319 PbI2, 489 PC60BM, 445 PC70BM, 447

614 PCDTBT, 449 PCPDTBT, 451 Penetration depth, 18 Penetration depth of light, 56 PFDTBT, 429 Phase evolution, 213 Phosphine, 194 Photo-generated electrons and holes, 110 Photon density, 5 Photon energy, 4 Photovoltaics, 256 Photovoltaics (PV) production, 169 Photovoltaics (PV) technology, 170 P3HT, 16, 437 P3HT:PC60BM, 439 P3HT:PC70BM, 441 p/i interface, 87 p-i-n a-Si-H solar cells, 293 Pin-hole, 189 P-i-n solar cell, 85 Planck’s constant, 4 Plasma Enhanced Chemical Vapor Deposition (PECVD), 86, 194, 256 Plasma ignition, 193 Plasmon resonance, 198 Plastic substrate, 576 Polarization analyzer, 189 Polarizer, 188 Polarizer and analyzer azimuthal angle, 191 Poly (3,4-EthyleneDioxyThiophene):Poly (4-StyrenSulfonate) (PEDOT:PSS), 452 Poly (Ethylene Naphthalate) (PEN), 587 Poly (Ethylene Terephthalate) (PET), 591 Poly (3-HexylThiophene) (P3HT), 437 Poly (Methyl MethAcrylate) (PMMA), 455 Poly (Methyl Methacrylate) (PMMA), 596 Poly (3-OctylThiophene) (P3OT), 443 Polycarbonate, 585 Polycrystalline CdTe absorber, 98 Polycrystalline film, 215 Polycrystalline film growth, 238 Polycrystalline grain size, 171 Polycrystalline thin film solar cell, 209 Polyimide, 170, 597 Polymer foil, 185 Polymer substrate, 202, 575 Poly {2-Methoxy-5-(2′-Ethyl-Hexyloxy)P-PhenyleneVinylene} (MEH-PPV), 435 Potential transmittance, 39 Power function model, 158 Poynting vector, 36

Index P-parameter model, 103 Principles of solar cell, 2 Process control, 250 Process monitor, 250 Process-performance correlations, 283 Process-property-performance correlations, 293 Property map, 179 Protection coating, 575 Protocrystalline Si:H, 83 Pseudo-substrate, 260 Pt, 545, 568 PTB7, 457 PTB7:PC70BM, 459 p-type a-Si1–xCx:H, 89 p-type nc-Si-H, 304 PV manufacturing, 170 Pyramid-shaped texture, 140 Q Quartz, 577 Quartz-tungsten-halogen, 189 Quasi-monochromatic, 41 R Real time SE, 116, 211, 255 Recombination junction, 283 Recombination loss, 23, 53, 55, 76 Recombination model, 50 Reflectance, 38, 85, 183 Reflectance of metal, 544 Reflectance spectrum, 111 Reflection loss, 23, 48, 76 Refractive index, 8 Resistivity, 102, 196 Resonance energy, 100 Reverse bias, 110 Roll-to-roll cassette, 186 Roll-to-roll PV, 170 Roll-to-roll speed, 192 Roll-to-roll technology, 186 Rotating-analyzer, 90 Rotating-analyzer ellipsometer, 118 Rotating compensator, 173, 221 Roughening, 238 Roughness layer, 196 Rough surface, 85 S Scaling factor, 65 Secondary ion mass spectrometry, 119 Sellmeier model, 576

Index Sellmeier term, 198 SE mapping, 181 SE mapping station, 175 Semiconductor, 84 Semiconductor deposition, 211 Sheet resistance, 107 Short-circuit current, 179 Short-circuit current density, 2, 84, 225 Si, 6, 9, 16, 322 Si-H-B p-layer, 266 Silane, 194 Silicon-carbon alloy, 86 Silver back contact, 91 SIMS, 119 SiN, 332 Single crystal CdTe, 103 Single crystal chalcopyrite, 116 Single junction solar cell, 256 Single-stage coevaporation, 116 SiO2, 86, 176, 328, 577 Si-PCPDTBT, 461 Si texture, 140 Smoothening, 238 SnO2, 86, 176 SnO2:F, 86, 176, 262, 519 SnO2 (non-doped), 517 Soda-lime glass, 86, 173, 212, 577 Solar cell, 1, 83, 210, 256 Solar cell performance, 256 Solar cell substrates, 222 Source temperature, 221 Space-charge region, 51 Spatial non-uniformities, 170, 256 Spatial resolution, 189 Spectral range, 204 Spectroscopic Ellipsometry (SE), 84, 169, 209, 255 Specular reflection component, 150 Speed of light, 4 Spiro-OMeTAD, 463 Stabler-Wronski effect, 63 Stainless steel (SUS304), 583 Standard deviation, 103 Steel foil, 186 Stoichiometric CIGS, 235 Stoichiometry, 221 Stokes parameters, 148 Stress-induced birefringence, 91 Structural evolution, 227, 255 Sub-bandgap absorption, 93 Submicron natural textures, 141 Submicron rough texture, 46 Substrate, 575 Substrate configuration, 84

615 Substrate shutter, 223 Substrate temperature, 225 Sunlight, 3 Superstrate configuration, 84, 257 Surface area model, 153 Surface roughness, 91, 198, 213, 255 Surface structure, 238 T Tail absorption, 9 Tail-state absorption, 62 Tandem a-Si:H/nc-Si:H solar cells, 293 Tandem p-i-n solar cells, 258 Tandem PV devices, 255 Tandem solar cell, 259 Tandem solar-cell structures, 161 Tauc-Lorentz model, 12, 320, 496 Tauc-Lorentz oscillator, 88, 278 TCO absorption loss, 76 TEC-15, 519 TEC-8, 519 Textured c-Si Solar Cell, 71 Textured solar cell, 43 Textured structure, 139 Thermal evaporation, 99 Thickness, 84, 256 Thickness evolution, 218 Thickness non-uniformity, 103 Thickness uniformity, 170 Thin absorber, 84 Thin film analysis, 84 Thin film photovoltaics, 83 Thin film solar cell, 83 Thin-film solar cell module, 141 Thinner absorber layer, 124 Three-stage coevaporation, 113, 210 Three-stage process, 44 Through-the-glass SE, 84, 169 Ti, 570 Tilt-angle SE Measurement, 143 TiO2 (anatase single crystal), 523 TiO2 (polycrystal), 521 TiO2 (rutile single crystal), 526 Top contact, 84 TQ1, 465 Transmittance, 40, 88 Transparent Conductive Oxide (TCO), 84, 173, 263, 495 Transparent material, 575 Tunnel junction, 265 Two-dimensional detector array, 170 Two-dimensional silicon CCD, 189 Two-step absorber, 89

616 U Uniaxial anisotropy, 428 Urbach absorption, 89 Urbach energy, 9, 100 Urbach tail, 100 V Virtual interface analysis, 260 Void content, 214, 259 Void fraction, 101 Void volume fraction, 178 Voltage-dependent collection, 110 W W, 572

Index Window layer, 92, 171 WO3, 529 X Xe, 189 XTEM, 109 Z ZnO, 113, 170 ZnO:Al, 113, 535 ZnO:Ga, 16, 533, 537, 539 ZnO (non-doped), 531 ZnS, 369 ZnSe, 370 ZnTe, 372